Without a model number you have me at a handy-cap. But let’s assume you have a single phase pump motor, Problem is I don’t know what type. Shuunt wound, Split phase, Capacitor start, PSC. Knowing it has to have a high starting load. rules out a couple.
From previous experience, I would guess that the motor has a centrifugal start switch inside. And this switch is failing. Again, with out the model number to determine the cost, I can’t advise you if you would be better off replacing or having it rebuilt. But with the rebuilding process you will be without it for a few weeks.