For me, I'd rather have fallout 3's system of loot than have mass effect's. Oh gods, the horror.
If you want a higher price for the junk weapons you pick up, *combine them* with repair. The returns on the first repair are worth the lost weapon, as low or no-repair weapons are practically worthless. If you're using a mod that lets you use assorted miscellaneous items to repair the weapon (such as tin cans, scrap metal, various other items appropriate-ish to the weapon), I'd even repair them as much as you can before selling them (plus you have a use for all that stuff besides giving them away for karma/money repeatable quests). Armor I generally don't even bother to pick up, since it's so heavy and difficult to repair.
If anything is truly useless, you can just leave it there. Of course, in Fallout 3, I ended up with a locker full of craftable/repair-usable items, and another of items to sell, and another with nuka-colas and nuka-cola quantums (for turning into quantums and then grenades later), and a desk with additional armor and things that I wasn't carrying around in it, and a filing cabinet with extra weapons that I wasn't carrying around, such as the fat man... In Mass Effect I ended up spending almost as much time in inventory management, turning items into gel, as I did playing the damn game. It got incredibly irritating after a while and actually led me to start and finish playing Halo 1 (which I had never played before, except the demo on the PC) instead as a break from all the inventory management, a game which I had avoided playing until now (this year, this month) mainly due to the lack of controllable saving and only having two weapon slots. I discovered that you really only NEED two, for a pistol (... for killing hunters and covenant in general), and either a plasma pistol or rifle (killing anything), a rocket launcher (flying things, tanks, the exhaust manifolds at the end), or shotgun (flood) as the situation dictates. So four would have been nice, but wasn't strictly necessary. After playing Mass Effect nearly to the end, You Can Only Carry Two Weapons, No Variations, No Upgrades didn't seem so bad anymore.