My concern is about yoyoing my weight

My BMI was 37 at my first weigh in but below 35 at my general practitioner (not bariatric) and my weight fluctuates. Will this make it harder to qualify? Do weights matter from other doctors I see?

The answer to your question is really dependent upon whether the body weight fluctuations matter to your insurance company.

Some insurance policies refuse to cover bariatric surgery if the insured person's BMI has fallen below 35 at any time in the preceding 5-year period, while other policies only look at initial prequalification weight.

And yes, any weight that is found in your medical record can count for or against you, regardless of which doctor or specialist obtained it, as long as your insurance is paying for these visits.

Wear weights and eat a heavy meal every time. Do what you gotta do.