two things factor into buoyancy, the rig, which is more negative with a full tank than it is empty by up to 12lb swing depending on size of the tank. LP104 is one of the biggest and most negative tanks, and is almost 16lbs negative when full. So using that
16lb tank
3lbs regulator
up to 11lbs for a bp/w *6lb plate, 2lb STA, 2lbs of cam bands, then about 1lb for d-rings, the webbing, and buckle
there's 30lbs right that, and that's just the rig. This is obviously worst case scenario
Dive is now wearing a 7mm farmer john because it's cold and they can't afford a drysuit. Those can be up to 40lbs buoyant. So you take of 15lbs from that because of the tank and bp/w, and you still need 25lbs of lead to sink. At the surface the wing is only keeping the 15lbs of the tank plus 12lbs of your noggin up, so it will be mostly full, but still able to keep you at the surface.
If the diver is diving shallow, they might be able to get away with a 40lb wing, but if they're diving any deeper than 70ft or so, a 40lb wing isn't actually enough to pick them up off of the bottom when the tank is full. At 70ft that wetsuit should still be about 20lbs positive, so you have 55lbs of ballast on between a full tank, the rig, and lead, less 20lbs of lift from the suit instead of 40, and you don't have the weight of your head, so you're at 35lbs of negative ballast at depth. That is where you need a 40lb wing.
Now, this is obviously the worst case scenario, drysuits are highly recommended at that level because the lack of buoyancy change with regards to depth is very useful for neutral buoyancy scenarios, and a cave filled LP104 isn't all that common of a single tank, though a Worthington 130 is, and those are 12lbs negative when full. Many people will use two different singles wings if they do warm water stuff and cold water stuff in single tanks, but typically if you're diving in cold water, you go to doubles and a drysuit so you aren't carrying lead around.
Same scenario above but in a drysuit. Rig is 30lbs negative, drysuit is 35lbs positive *made up number*, need 20lbs of lead for balance purposes. Get to the bottom, and you have 50lbs of ballast, against 35lbs of buoyancy when full, so you can get away with a smaller 30lb wing *still have to factor head at the surface*.
When you are carrying things up from the bottom you should always use lift bags if they are more than about 5lbs, anything more and it can cause serious problems for you on ascent and is dangerous. Lift bags are relatively cheap and you generally aren't picking things up from the bottom. This is why you inflate an unconscious divers bc to get them neutral for retrieval instead of your own. Not safe otherwise.