^^^ If you try to catch more gas to have a larger volume to weigh, then the apparatus gets accordingly larger and heavier. The required resolution of the scale stays the same.
Well, how did the physicists of the 18th-19th centuries measure or weigh anything, without the equipment we now have?
This was kind of like the supercollider of the day. Weights and measurements were the actual research, and a whole lot of work was done on it. Clock makers were developing fine machining, so naturally some of that could be applied to precision scales.
From this work, much was learned about volume and mass. Right away, the metric system was designed with this in mind. And of course the table of elements was based on molecular weight.
All of this was derived and inferred by super clever methods, like measuring gas volume (which is easy) at a certain temperature and atmosphere.
BTW, if I recall, our experiment took the long tube and we filled with water and acid and inverted it onto a piece of metal which dissolved. I think our lab test was to discover what gase(s) were given off by the volume produced.
It is hazy. I was really into chemistry but after some of this mind numbing computation, I decided to go into computers instead.
One last memory: my stupid lab partner decided to siphon the water out of the trough. Don't ask me why. The water had diluted acid in it. He ended up talking about his "clean teeth" the rest of the semester. Nothing like a little hydrochloridic acid bath to get rid of the plaque.