Why not build bigger dreadnoughts?

Again, you analogy is out of whack.  Dreadnoughts on earth were battleships with bigger guns that enabled them to fire on enemies from a greater distances.   However, projecticals on earth are affected by friction and gravity.  As we learned in ME2 on the Citadel, in space a projectile will travel indefinitely and "ruin someone's day somewhere" if it misses it's target... So, any ship of any size can fire at a long, long distance as long as their computer can accurately work out a firing solution.  So, in the ME universe, a bigger gun would do more damage, but not enable the ship to fire from. a greater distance.

On earth, the concept of the super-large battleship pretty much went the way of the dodo after WWI.  Contributing to it's demise was the rise of the aircraft carrier.  Some classes of dreadnoughts were also armored in such a way that their decks were also susceptible to enemy air attacks and attacks from projectiles being fired from longer distances (i.e. on an arc).  Aircraft carriers are large so that they can house more aircraft and aircrew.  They are efficient as mobile fighter launch bases and that is why countries still invest in building them but do not invest in building dreadnoughts.  The advent of guided ballistic missiles fired from smaller, more stealthy ships (e.g. subs) are also more efficient than the old dreadnought.

Since Shepard and crew escaped the geth dreadnought in a geth fighter, it is likely that the geth dreadnought was more akin to an aircraft carrier than a dreadnought (although Bioware seemed to enjoy using the term "dreadnought" to describe any larger vessel in the ME universe).  Far tougher to blow a bunch of fast, mobile geth fighters out of the sky than one ship firing on you from a distance.

In addition, the geth dreadnought is using Gardian anti-fire lasers.  If you bring EDI on the geth dreadnought mission, she will further explain that the dreadnought "is using "ultraviolet frequencies instead of the standard infrared" to which Shepard will respond "Expensive. Bet it gives them an edge in close combat."  Tali indicates that it was those lasers that "carved right through" the shields of the Quarian ships that rushed the dreadnought.  It's superiority is not about distance (as you suggest), but about accuracy.  Also, Tali later indicates that it is the geth's "planetary defense canon" that was ripping through their fleet... so, it seems obvious that the Quarians were not just engaged with the dreadnought, but also with the defenses on Rannoch itself.  We also later find out from Legion, that geth squadrons from the server were also inflicting heavy losses on the Quarians.

The Nexus has a different purpose... to bring as large a population as possible to Andromeda... so deciding to invest in it would involve a totally different set of considerations than investment in a dreadnought.

Indeed. Imagine a 10km dreadnought(about the size of the Crucible) trying to maneuver to align it's main gun to shoot at a enemy fleet or trying to maneuver to avoid incoming fire? And what about the amount of fuel (antiprotons) to run its engines or all the eezo to power its FLT drive and kinetic shields?

Sure if it hit a target it would probably destroy it on a single hit but the drawbacks are too many to make it viable.

That weapon was also destroyed so it's really not a pure conjecture that the drawbacks outweight the avantages.

We actually have evidence of super massive weapons being affective: that what took a reaper down is some long forgotten cycle (although I think it was on a planet, which doesn't change that much).

That weapon was also destroyed so it's really not a pure conjecture that the drawbacks outweight the avantages.

I believe that was only possible because the Reapers were ill deployed and it was a kind of suicide tatic. Not really sustainable.

Where do you get that a bigger gun is necessarily a faster gun?... because it's not.  If you watch the Earth battle, you can clearly see that the big guns are the slower ones in that battle.  Even the Reaper lasers are very slow-firing weapons, needing to recharge between hits.  That's why Shepard can take the one down on Rannoch.

Also, iRL dreadnoughts on earth did not carry smaller ships (other than boats that would just take on survivors if a ship was sunk or deploy a boarding party).  Deploying smaller warships was not their purpose.  The purpose of an aircraft carrier IS to deploy aircraft... so, as I said, it's made larger so that it can carry more aircraft and crew... not to make it be able to fire directly at enemy locations from a distance farther away.  The geth dreadnought did carry geth fighters.  The comments about the fire power to the dreadnought DO NOT talk about longer range encounters.  They DO mention "close combat."... so, again, your analogy is out of whack on that front.

Also, I don't think the Destiny Ascension was the Asari's only dreadnought.  I don't think the geth dreadnought was their only one or that the Turians, etc. didn't have dreadnoughts of their own that we never see.  During the battle for earth, another ship shaped like the Destiny Ascension is seen farther back in the pack of fleets. 

They built the Nexus as large as they could so that it could house 100,000+ people once they got to Andromeda.  There is also the possibility that the size was needed so that it could eventually be completed as a Mass Relay capable of connecting to the Milky Way.  They could have perhaps sent everyone in the AI on the one ship instead of one the 4 Arks, but they probably didn't want to do that in case something happened to the Nexus... better to split one's eggs among a few different baskets.  They probably made the Arks species specific because of the different requirements different species would have for being in stasis.

That's like saying we don't need aircraft carriers, we can build airports on land. 

Also, the IRL dreadnought vs. the carrier has everything to do with Mass Effect.  The Treaty of Farixen mirrors the Washington Naval Treaty signed at the end of WWI.  Carriers were not subject to the same restrictions as dreadnoughts under the Washington Treaty and they are, likewise, not subject to the restrictions set out in the mythical Treaty of Farixen.  So, IRL, countries invested in carriers rather than dreadnoughts after WWI, so it seems reasonable that the navies of the ME Universe are investing more money in carriers than dreadnoughts as a means of getting around Farixen.

A platform is cheaper, doesn't require accommodation for a crew and can be remotely operated or even automated. It's just need to be towed to move it where you wants.

A Dreadnought will usually host a fleet command center, has provisions for long trips and many marines on it.

You're still not following.  The Treaty of Farixen limits the number of dreadnoughts a species can have based on the number that the Turians have.  However, the other races want more ships overall, so they build carriers (defined under the treaty as large ships that DON'T have that big gun).  Technology advancements, as a result, go into those carrier class ships and the dreadnought tech just sort of stagnates.  It is part of the reason why the dreadnought became obsolete IRL.

The other factor is that at longer ranges, your projectile (unless it is guided to change course) can be tracked for a longer period of time... giving the target a bigger opportunity to either destroy your projectile or move out of its path.  There would be a threshhold where fighting from farther away would become a liability, not an advantage.  It's a balancing act... what is optimum is not always the largest projectile fired from the farthest distance away.

Why not build bigger aircraft carriers?... because, again, you want to build more aircraft carriers so that you can spread your forces over a larger area and deploy them more efficiently to locations near where the carrier is located.  You have to consider that they may have to defend more than one location and those locations may be very far apart from each other... so, you would station your carriers in different parts of the galaxy so that the nearby ones could respond quickly and then, if necessary, you could pull in the ones from farther away to reinforce the fighters already engaged in the battle.  It's more about balancing size vs. speed of deployment than shear firepower.