But I think you'll end up more than the 2-6lb negative that you're expecting...
Assume you're dead-neutral at the surface, with an empty tank.
If you've got an 80cf tank (steel or aluminum, doesn't matter), then at the start of the dive, at the surface, you'd be 6lb negative, just from the extra weight of air in your tank. For a 120cf tank, this would be 9lb.
You said you use a 7mm suit. My new 2-piece 7mm has about 20lb of buoyancy, pretty much all of which goes away by the time it's down to 60'. So if it's neutral at the surface, I'd be 20 negative at depth. Now if you only mean a 1-piece 7mm, you could probably halve that, depending on make, manufacturer, how big you are (a larger suit has more neoprene, which means a larger swing), how old it is (old suits compress a bit), etc.
So at depth, at the start of the dive, you could be 16 to 26 lbs. negative... A lot more than the 2-6 you asked about.
As for how much you can swim up... I'm an ex-lifeguard, in good shape, and have a strong eggbeater, and find:
10 lb: fairly easy. Most strong swimmers can handle this, although it's beyond what a lot of average swimmers can handle.
20 lb: takes effort. Certainly I wouldn't want to have to go more than 20-30 feet. Some lifeguards have difficulty with even this much.
30 lb: Quite hard. This is about the top weight I can consistently lift, and that still involves pushing off against the bottom of the pool, and only going another 6-10 feet.
40 lb: Only on a good day. A *very* good day. And even then, I'm jumping off the bottom of the pool, and just barely maintaining upwards momentum. I doubt I could do this from a hovering start, let alone if I had downwards momentum. It's also dead-slow. About 20sec, swimming as hard as I can, to get from the bottom of the pool to the surface, and it's only a 12' deep pool.
All of these are also based on using a kick called "eggbeater". A very slow kick, but one that provides quite high thrust... And not a kick I think you can do wearing fins (though I've never tried).
Practical upshot: if you're in good shape, and fairly shallow, you can probably swim 10lb. Anything more gets unlikely.
Jamie