It usually is because one side gets more sun than another. Such as flowering plants along a fence line. With plants close by other shrubs and trees and dealing with root competition, they seem to flower stronger on the side farther away from the competition. Also, I’ve read that it can be caused by uneven light when the flower buds are forming. Thinking back to spring, was the light even on both sides? Also, give consideration to the roots and fertilizer. Is it possible one side is taking up nutrients better than the other side? Oh, and don’t forget pruning! Were the flower buds pruned off or damaged on one side? I hope these ideas help you find the cause and help with a solution.
Thanks for writing!