In order to float, the buoyant force must be greater than the weight. Here's a diagram:
This all happens because there is a pressure difference between the bottom and top of the balloon (P = F/A = ρgh). Although this effect may be appear to be relatively negligible in average balloons, it is heightened when you take into consideration the large size of the Macy's balloons. It is easy to think about this phenomenon: there is a lot more pressure at the bottom of a pool than at the top of a mountain. So, the bottom of the balloon experiences more pressure than the top- pushing the balloon upwards.
This is also why so many people are required to hold the balloon down!