Free DLC?

Yes, I believe they were.

ME2 is sort of weird in that some of the DLC is listed through the main Xbox Live connection (LotSB, Kasumi, Arrival), but some of it is no longer there (or perhaps never was due to it being part of the Cerberus Network).

Zaeed and Normandy Crash Site aren't listed there; and to access the listings for them, I have to boot the game and go to Downloadable Content option in the main menu. Both are listed there and the price is shown for both as "Cost (Microsoft points): 0" When selected, it goes to a normal Xbox Live purchase screen that shows the Price as being "Free."

Comparatively, the listing in that location for Kasumi - Stolen Memory shows "Cost (Microsoft Points): 560"; but if I select it, the normal Xbox Live purchase screen also indicates that the Price is "Free." - However, that seocnd screen screen may just be reflecting the fact that I've already purchased it.

Depends on what weapons packs you're referring to.

Here's the List of DLC from the Main Menu of My Game that Show "Cost (Microsoft Points): 0"

Normandy Crash Site
Zaeed - The Price of Revenge
Cerberus Weapon and Armor
Firewalker Pack
Cerberus Arc Projector

I believe these were the DLC available through the Cerberus Network.

Here's the List of DLC from the Main Menu of My Game that Show "Cost (Microsft Points): 160, 560 or 800"; and I believe these were the ones originally offered outside the Cerberus Network.

Alternate Appearance Pack 1 (Garrus, Thane, Jack)
Kasumi - Stolen Memory
Equalizer Pack
Overlord Pack
Aegis Pack
Firepower Pack
Shadow Broker
Alternate Appearance Pack 2 (Tali, Grunt, Miranda)
Arrival
Mass Effect 2 Genesis

As I said, I can't tell whether or not they are now Free to new buyers, since once something is purchased the detail purchase screen in Xbox Live always changes the purchase price to "Free" to indicate that you can redownload it if you have to without being charged again for that item.

I didn't buy any of the DLCs, so everything I have was given for free, and those are:
Collector's Weapon and Armor
Recon Hood
Sentry Interface
Umbra Visor
Firewalker Pack
Cerberus Arc Projector
Cerberus Weapon and Armor
Zaeed
Cerberus Network
Normandy Crash Site
Blood Dragon Armor for Mass Effect 2
Terminus Weapon and Armor

I recently logged into Origin as well and noticed that the following were free though in the past when I would ask for these DLCs from EA live I was told they could not grant them. The Xbox versions are also available

Recon Hood (Dr. Pepper)
Sentry Interface (Dr. Pepper)
Umbra Visor (Dr. Pepper)
Terminus Weapon and Armor (Retail Preorder)

Previously the only way to receive these items were on PS3

Inside the game, under and right of the main menu, there should be a button to connect to the Cerberus Network, which is a free DLC by itself.
I'd have thought after all this time they'd release a patch that removes the need for it, but I guess EA have other plans.

There should be a "connect" button next to the Cerberus Network one, which is press-able.

Are you playing on an Xbox console?  If so, you may still need to dig up the activation key in your disc packaging (I know I had to use it when I first activated the Cerberus network a couple of years ago.  As I recall, I also had to activate it through the "Addons" screen in the Xbox Marketplace... and I'm thinking the Microsoft has never changed that part of it.

If you don't have the activation key, I don't know... maybe try just a straight download of the Cerberus Network from the Marketplace (i.e. maybe it won't ask you for the activation key now).  I can't test it because, for me, it's showing up as an item I've already downloaded to my account.

ETA:  Scratch that - I see now you're on PC.

I don't think playing ME on PC is a bad thing (you have access to mods and such that I don't).  It's just I"m sorry I can't help you since I'm on the Xbox 360.

I'll try to add ME2 into the firewall exceptions. I also sent the email to their support, so maybe there is some easy way to make things work...

Adding the ME2 and Origin to the list of the antivirus exceptions allowed me to connect to Cerberus, and the game stopped complaining on the start-up that it cannot access the DLCs. I so far cannot see the Zaeed's Mission in my Journal. I am guessing I will have to start a new game for them to activate, or they will pop up at the next major area change/assignment swap?

EDIT: And, yes, everything showed up on the major assignment update.

Thanks for help, everyone.