I'm fairly overweight
(BMI of about 29) and I didn't have an issue, my Endo didn't even mention my weight!
I'm sure it depends on your doctor so it may be possible your Endo will tell you to lose weight first
I hadn't even heard of weight ever being an issue with T
Edit:
Oh! And what the above user said about T!
It does make it easier to lose weight so look forward to that! Though personally for the first like two or three weeks I just go like ridiculously hungry and gorged myself haha
I also had a lot more energy so it balances out