Some DOT spec bottles are heavier. A lot aren't though.
In salt an empty Ali 80 with reg (mk25 or equiv) attached will rise up a line IF you give it a good shove to get it going. In fresh it may well hang around once it loses momentum.
Not arguing that the bottle is not marginally positive when empty. Leaving 15 to 20 bar in them is of course better for the gear.
However, without dick swinging I have genuinely have lost count of how many empty bottles I have lugged at one time (i do recall having at least three leashes each with three empties plus a couple of floaty scooters and feeling like the guy selling balloons at the fair) and not once have I found it to be an issue if the bottles are stored on leashes.
Mind you, I weight myself for empty cylinders and no stages. If I did weight checks with full gas load then of course everything empty would bring issues.
Edit. To clarify, I weight check by descending to 6 meters with extremely low levels of gas (20-30 bar) then get neutral and remove swueeze from suit. Then ascend to 3 meters fumping to get neutral again and check how much gas in wing. This translates to lead on a litre per kilo basis. This is, to me, more accurate than descending to check as you can't empty your suit as efficiently on ascent as you would descending.