Congrats!
I'm really heavy as well, and I was referred to a nutritionist by my endo to help me lose weight. Overall my blood pressure and my bloodwork checked out, other than my cholesterol being slightly elevated.
I don't think there's much that can affect whether or not you're able to start T, but some things can affect the dosage.
The thing that got me on a super low dose was PCOS. I already had high testosterone, and since I had PCOS and was at risk for certain diseases that T would put me at risk for even more, my doctor erred on the side of caution.
My doctor prescribed the T before she got my blood results back, so unless you have some sort of condition like PCOS, you should be put on a low-normal dose, and after a while of adjusting it should be upped. That's just my experience!