“How fast does sleep apnea progress?”

There are multiple answers to this question; many variables including weight gain, etc. It is usually a slow process but it gets worse over time unless there is weight loss involved. A better answer could be formed with more specifics of each individual case.

I do not think that is the best way to think of the problem. Apnea in children is generally related to size of the tonsils, shape of the mouth and nose, and weight. Those things do not change very quickly on average and so apnea tends not to change much over a short to medium term. Losing or gaining a lot of weight would affect apnea with weight gain making it worse. The anatomy of tonsils and nose is generally pretty stable. If there is apnea in children, there are multiple reasons to get it treated including better school performance and lower long-term health risk.