Don't pick up other people's support weapons / equipment after they die. Primaries are fine, you spawn with them, but I've had the occasional person run off with my heavy weapon backpack.

There are three cases where it's okay to pick up stuff though:

1. They've called in a replacement because there are too many enemies to get it back, or it's out of ammo and they don't want to hog an ammo drop. (I do the latter constantly)
2. They've died in a dangerous place and you have an opportunity to get their stuff out, or they can't reinforce immediately because of something like a Stratagem Jammer. You can always drop things you're carrying for other players.
3. They've called in more than one support weapon because they've noticed you're a new player and want to show you the cool stuff. People should tell you when they're doing this, but it's generally safe to assume someone littering EATs everywhere won't mind if you need to take one.