You have a bench (image), where would you sit to maximize the reaction force on one end?

The bench is not bolted down.

Intuitively I believe the answer is when you’re sitting right above one of the legs - but I cant seem to figure out a way to prove it mathematically.

The right answer is too actually sit on either the far left or far right, on the very edge of the bench; not over one supported end. By sitting on the very far end you can put almost all the reaction force on one leg. If your heavy enough you could reach the point where one leg has no reaction force at all or flip the entire bench over.

It would be your weight x the lever arm