My deflated birthday balloon

After two months my birthday balloon is sinking. These balloons are made of aluminium rather than rubber because the gaps between molecules in rubber, whilst small enough to stop air molecules escaping easily, are big enough for the tiny monatomic helium to get through. The gaps in aluminium are smaller but the helium escapes gradually. I was expecting that there would come a point that the weight would be bigger than the upthrust and the balloon would sink to the ground. Upthrust is equal to the weight of air displaced and that depends on the density of the air. This suggests that the density of air in the room is not uniform and is lower nearer the ceiling. So there is a density gradient. I suppose it's a bit like the Galileo thermometers.