Weight loss after BBL: Can I gain the weight back in my butt?

Fat injection is performed in diferent ways. It can be placed below muscle tissue or above it. When its placed above muscle tissue it behaves like all the fat tissue im your body, therefore if you gain weight you might as well feel it in you buttocks aswell. That mechanism doesnt happen as much when the fat is placed below the muscle.

We don't know how our bodies will react to weight gain. We could expect the buttock to get bigger as the fat cells will multiply. 

You've asked an excellent question regarding how fat after BBL behaves. The short answer is that once the fat has established a blood supply and is viable (alive) after a year, it should last for many years and act just like any other fat cell in the body. If you lose weight, you lose weight throughout your body more or less including the transferred fat to the buttocks so that the cells shrink. On the other hand, if you gain weight again, the transferred fat cells (just like any other fat cell in the body) will expand as the calories turn into lipid (fat) that are stored in the cells. I hope that answers your question and you can expect to buttocks to enlarge as you (carefully) gain weight.