How can I pick up dropped weapons?
Weapons are picked up automatically just by running over them - but they will only be picked up if you are not already carrying a weapon of that type. You can only carry one weapon of each type - pistol, rifle, SMG, MG, and Heavy - and you can't drop or swap them in singleplayer mode.
However, if you enable cheats, you can equip any weapon you want. See this page
for instructions on that.