Will gaining weight cause the fat transferred to my hips to get larger?

The transferred fat will behave just like the surrounding fat cells--decreasing or increasing in size as your weight fluctuates.  Nevertheless, it remains important that you maintain a healthy, stable weight through superb diet and regular exercise. Keep in mind that the results of body contouring surgeries such as BBL can change by yoyo weight. I hope that helps.Dr. Tarick SmailiCalifornia Surgical Institute 

Remember with a BBL, it is fat that is being transferred.  As a result, as you gain weight the areas where the fat was transferred will get bigger and as you lose weight they will get smaller.  You absolutely can work out after your BBL, but you must be careful to keep your calorie intake up to prevent losing weight and fat in your but and hips.

​Hello dear!!
Thanks for the question and provided information as well.
After liposuction, the areas treated are not likely to regain fatty fullness, as many fat cells have been removed. These areas have reduced fat storage capacity.
However, if weight gain occurs, the fat will be mostly stored in areas that have not been liposuctioned. ​It's hard to know for sure how weight gain will affect your body, ​this is why you should try to eat healthy and exercise on a regular basis, so you can maintain the results long term.
Lifting, squats and lunges after a BBL will only help increase muscle bulk and definition and achieve a more projected buttocks.
Hope this helps. Good luck :)