It is actually connected to your bladder and it remains the same length regardless of how much weight you gain. You can convert an “outie” (protuberant) belly-button to an “innie” (deep) belly-button via a plastic-surgery procedure called an “umbilicoplasty”.
I am occasionally reminded of how interesting it is that we do not lose our naval/belly-button over time. All eight-billion of us are walking around with a physical anomaly that has served absolutely no function at all since we were brought into the world. Unless you happen to have a piercing there, we are blind to it most of the time.