Why are there variations in atmospheric pressure how was this proven?

Why do your ear pop when trebling to different altitudes?

We have cold fronts and warm fronts. Cold air weighs more than warm air (technically that isn't right--I should say cold air has a higher density than warm air) so the air pressure varies. Why as we go up do our ears pop. As we ascend, the column of air at higher altitudes has less weight than when we are on terra firma at sea level so the pressure INSIDE the body is higher than the pressure OUTSIDE our body. We must open our mouth to equalize the air pressure and that makes our ears pop.