Current Balance in a Nutshell: All Guns are Caster Guns, and All the Powers are Weak.

The idea behind the whole weight system was to give the players a choice, a tradeoff. Sure, your Adepts, Engineers, and Sentinels can now use any gun they wish!
But we can't have the classes that are supposed to use their powers to damage also have excellent weapons, making the poor classes that rely on their weapons in the dust.
So it was decided that if they wanted to have the really powerful sniper rifle, the assault rifle that tears through mobs of enemies easily at short and mid range, or a shotgun with massive stopping power they would have to take longer cooldowns to compensate.

This isn't happening.
I can take a Vanquisher X on any given class with no cooldown penalty. Slap some ULM on that bad boy and I can also take a light secondary weapon as well.
There also doesn't seem to be a whole lot of difference between one class's carrying capacity and anothers. At this point that matters little anyway.
Classes with greater carrying capacity only benefit by being able to carry an extra weapon. Its nice, but how much does that really increase how much damage you can put out?

The weight system I think is a pretty critical part of balancing this game, it needs to matter. Right now, it doesn't matter much at all.
There needs to be a much bigger difference in class's carrying capacity, I'm mostly thinking reduce the carrying capacity of more castey classes such as the Human Engineer and the Asari Adept
There needs to be a bigger difference in the weight of the weapons, especially the assault rifles. Rifles that benefit greatly from Turbocharge should be heavier and deal more damage than they currently do (Cyclone, for instance)

With that in mind, the base cooldowns of most of the powers in this game need to be *slashed*, hard.
The Asari Adept, for instance, should only cast powers as slowly as she does currently when she is carrying a Revenant, a Venom, or a Vanquisher.
If she's carrying a Mattock, a Disciple, or a Viper she should be able to cast faster than that.
That way an Asari Adept with a Vanquisher is still... okay, but with a lighter weapons she becomes almost as good as the N7 Fury was (just gotta give the BE's the ability to give her shields back instead of melee doing it)

When you can put almost any weapon on a cast heavy class, if either the weapons or the powers are good you're going to give either the caster classes or the weapons classes a sharp edge over the other.

If the powers are bad and the weapons are bad, you have this game at the moment. The most obvious exception to "The guns are bad" is the Vanquisher, and its pretty optimal at this point to put a vanquisher on any class you have.

When casters aren't able to use the exact same weapons as Soldiers and Infiltrators without penalty then you are free to make powers actually good or weapons actually good without either trivializing the game or making one subset of classes significantly better than the other.

Anyway, that's the gist of how I see this game. Everything is just uniformly bleh as far as player options go.

EDIT:
I typed this late at night, and my ADHD meds wore off hours ago. I'll edit this in the morning and make it a little less like a mind-wandering rant