As always, there are no simple answers, but there are simplifications. Yes, the impulse from the escape wheel on the pallet is transferred to the crutch and then the pendulum. And if the pendulum bob is too heavy, that could lead to the clock stopping. But, if the pendulum bob is correct, that doesn't mean the solution is to use a lighter pendulum bob. The stopping means there isn't enough power, which could be for a variety of reasons, and that needs to be corrected. You could try a lighter bob and that could help confirm a low power diagnosis (as opposed to say teeth to teeth interference or some other issue). It's sort of like adding more weight, which would maybe also work, but not be in accordance with the original design and will lead to more and quicker wear. Ideally, we want to find the source and fix that, not use compensating approaches. Sorry if I sound preachy. I just to make the point that while band aids may be a quick fix, they should not be left on forever.
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Tom