Robin, welcome!
You've come to the right place to get support and community while you figure all this out.
Body dysmorphia and gender dysphoria are two quite separate things, and you could certainly be suffering from both. I agree that talking with a therapist would be really helpful in sorting out your feelings. It's great that you've had the courage to come out to people. That's a huge accomplishment, and at the same time, I think that doing something that scary can bring all one's insecurities and self-doubt to the forefront of one's mind: no matter how well it goes, it still makes you feel very vulnerable.
Your size is definitely not a barrier to a successful transition. There are plenty of big guys out there, and they do just fine. For me, transitioning has helped me deal with my own body dysmorphia as well: I've found that the possibility of having a body I'm actually comfortable in, gender-wise, is a big motivator for working out, eating better, and doing what I can to get my body closer to what I'd like it to be. I'm never going to be a stud, at my age, but "presentable geezer" seems well within reach.
But as others have said, the main thing is definitely to explore your own feelings and work out what's right for you -- it's an ongoing process for most of us, I think.