Kate, the seat switch being damaged can be from many reasons and not just due to the operator being a lightweight. Believe me, I have a very LARGE basis for my observations on my own tractor.

More likely is the shifting position of your weight also shifts the switch slightly and it momentarily loses contact. The easy way to prove it's the switch is with a jumper bypass, but there is absolutely nothing on the brake pedals that is electrical to cause a problem. Your parking brake lever has a switch, but the brake pedals don't unless you have an HST with cruise control. In that case, the brake pedals will de-energize the cruise magnet, but that circuit is completely isolated from anything that would kill the engine. So I am firmly on the same team as RickB in saying it's your seat switch.
BTW: On my tractor, the parking brake has to be engaged AND the shift lever in Neutral for the engine to stay running when the operator leaves the seat. I think yours is the same. The parking brake will not bypass the safety if the transmission is out of neutral.