Also ... if you think that PCs won't grab anything they can, I really have to wonder who/what kind of games you've been playing with.
People that didn´t start out playing dungeons and dragons and other such loot centred games.
Just make it pretty clear for the players that unless that they can come up for a reason as for why they should take something with them do they really not have to loot since it isn´t fitting into the setting, as said in another thread, either is the loot from heritics, owned by other parts of the emperium that wants it back, or from xenos, take your pick of who and how you will piss people of.
Beside that and even more of topic than it already is, throw some limitations on how much they can take with them (1 melee, 1 pistol, 1 basic, 1 "light" armour and 1 grenades with 3 reloads for all things that need that, each other thing that they want costing a point from their combined Strength Toughness stat bonus pool. That is at least how we play.) and you will quickly see them behave.
And back to the subject, there is a single pyromancer power that makes one ignore both toughness and armour... maybe is it time for them to meet a psyker of that school
Seizure to better kill heretics/xenos, to give to AdMech/whoever to study, to examine for information, to run past the records for use in prior activities/events, to deny access to any that haven't been dealt with yet, for use in undercover/deniable operations, give to the AdMech to pacify the machine spirits for having been misused, etc. There are all kinds of good reasons why taking everything you can carry and examining them in detail back at base is a good idea - anything not needed can be allocated to the Acolytes/Inquisitor's version of the Arbites Cold Vaults - the Arbites collect weapons used by recidivists/heretics/xenos/etc that they deal with and keep them in vaults, they serve as a ready resource for research and training, as well as for supplying undercover agents/teams, and the occasional Inquisitor/Judge stops by to see what's been captured recently. Trade them into the quartermaster for goodwill or better stuff.
Knowledge is power. Examining the weapons of your enemies is generally going to be a good idea - if nothing else, it gives you information on how well resourced and backed they are, and at least some of the weapons may be traceable to other events/activities, or other people.
Also ... there is absolutely no way I can believe that anyone would leave valuable items lying around where the next person to walk by could grab them. Nor can I believe that an Inquisitor would be particularly pleased with a team that just left stuff lying about all the time - sure, maybe they don't haul it back themselves, but when possible, calling for a retrieval/verispex team to take a look at things and clear out the stuff and the bodies. True, some of it might well be returned to the rightful owner/heir, but it's going to be examined to be verified clean of taint (be it xenos, warp, heretekal, etc).
Sure, the players very well might not utilize very much of the stuff they grab, but there's no good reason to leave it in circulation for the next batch of lunatics or criminals to get their hands on.
On the carrying stuff ... playing by the weight limits actually works reasonably well. Also, if a GM ever tried to limit what players could have with them that bluntly/crudely on a regular basis, I do not know anyone who would put up with that for long. I can understand making players explain where they're carrying everything, which does a pretty solid job too.