You can find quite a few heavy weapons throughout the game. Here's a list including what you have to do to get them:
M-100 Grenade Launcher - you can find this one while escaping the Lazarus station at the beginning of the game.
M-622 Avalanche - research in Normandy lab (you need two upgrades in Heavy Weapon ammo to unlock and 15.000 Iridium to build).
M-77 Missile Launcher - research in Normandy lab (you need one upgrade in Heavy Weapon ammo to unlock and 5.000 Iridium to build).
Collector Particle Beam - you can find it during your mission on Horizon.
M-920 CAIN - research in Normandy lab (you need three upgrades in Heavy Weapon ammo to unlock and 25.000 Iridium to build).
M-490 Blackstorm Projector - part of the "Terminus Weapon and Armor" available in the PSN store.
M-451 Firestorm - part of "Zaeed - The Price of Revenge" (Cerberus Network). Found during Zaeed's mission.
Arc Projector - part of Cerberus Network.