I only became hypo 12 years ago and one of my symptoms was high blood pressure. It happens every time I need more medication. Doesn’t matter my experience. What does matter is I gave you a link from a reputable site. Your one experience doesn’t discount my experience, and the experience if many people I know. Read the link. Google hypertension and hypothyroid. You usually appreciate medical and scientific facts. Hypertension is secondary to a lot of conditions. Plus, I don’t understand what year you developed Graves disease has anything to do with anything.
I said in my answer I doubt the OP has a thyroid condition, because I can’t imagine he hasn’t been checked for it. The OP has had hypertension since teen years. I would assume he has been checked for diabetes and other common diseases that often happen in conjunction with high BP. If he is overweight, I would be pretty sure the doctor told him to try losing for multiple reasons, including BP.
Why are you harping on my answer. Because of you this Q is now several posts about thyroid, which is ridiculous. It was just one mention about my experience, and often overlooked by doctors, within other suggestions. I talked about genetics too. I have a girlfriend who has a beautiful figure, works out 5 days a week, eats well, and has to take BP medicine. Her body just doesn’t regulate well regarding BP. There doesn’t seem to be any other explanation. She’s been taking meds for many many years. It runs in her family.