Weapon stabilizing
As originally highlighted in BCM93 which was recorded in the snow below AOTCR's twin bridges, dropped weapons can actually slowly move of their own accord. Or maybe they're not necessarily going anywhere but nevertheless appear agitated, a condition from which motion may perhaps develop. Either way, we're talking about weapons being unstable. 'Stable' is when you see no motion or agitation at all. The full story on this phenomenon is unclear to me, and certainly I haven't attempted a systematic investigation, but it may be limited to certain areas or situations.
Another place I've had unstable weapons is in the early part of level 8, where it was significantly affecting my set-up work for the pyramid megabattle and pyramid descent fight. Both of those scenarios potentially involve harvesting early dropped covie weapons, and I noticed that such weapons were quite often moving.
Part of the trouble with such a weapon is that you may actually end up losing it, namely if it's sinking. If it sinks far enough, you lose sight of it and ultimately might not even get a pick-up prompt for it. I'm pretty sure that's how I lost a plasma pistol, in one of my set-ups. Just couldn't find it any more!
Another drawback is that if a weapon is rising, it can eventually appear to be floating, such as was the case with one of my spare needlers in BCM556, as seen around 4:39 That one hadn't risen far though. For a much more radical floating needler, this time in AOTCR, see my dedicated movie BCM491.
Stabilizing an unstable weapon
Because of the drawbacks, you may thus be interested in stabilizing a weapon. How to do it? Pick it up and drop it, then watch closely for movement or agitation. Movement is usually quickly noticed in the form of evolving 'jaggies' along edges, and although you don't need a magnified view such as offered by a pistol or sniper rifle, certainly it can make things more easily seen. Sometime there can be movement or agitation but i ends after a few seconds. If it seems to be be continuing however, the operation has failed. Just repeat until successful. Based on my experience in level 8, I'd say you're likely to stabilize the weapon before long, although it could take several tries.
An alternative to picking it up and dropping it is to shoot it, e.g. with a plasma weapon or pistol. But again, it may take multiple tries.