Well, the reason you're getting confused is that the question is misleading
A pound of ice and a pound of water have the same weight but your mind is conditioned to picture them and you know that ice and water have different densities. While a given pound of water and a pound of ice would have the same mass, the volume would be different. The water would have a greater volume, because water is more dense than ice (which is why ice forms at the top of a lake).
The situation with gases is a little different. When you heat a gas, you don't change its mass. (Wow, that rhymes. :)) The speed of the molecules bouncing on the balloon increases when you increase the temperature and so the density changes (because the volume changes). This change in density causes the balloon to rise, because the hot balloon is less dense than the air around it. Likewise, a cold balloon falls because it is more dense than the air around it.
(In other words, if you ’weigh’ the baloon, what you measure is not its total weight but the difference between its weight and the weight of the air it displaces. So that depends not just on weght but also on volume. When you weigh water or ice in the atmosphere, either one is so dense that the weight of the air they displace isn’t very important.)
I hope that this explains this common trick question and why it is so confusing to everyone.
(published on 10/22/2007)