The closest thing to consensus for transition is the WPATH Standards of Care, and they warn of two potential problems with being overweight and undergoing masculinizing therapy: a potential increased risk for high blood pressure and development of type 2 diabetes, both of which are complications already associated with being chronically overweight. There’s also a fair chance that your friend will gain some weight when he begins T.
Having said that, HRT is generally stressful for a body, and losing weight in general is a good idea for overall health while transitioning. Most therapists will encourage this, both for the health benefits and for the increased self-image and self-esteem that weight loss brings to the transitioning man or woman.
Where your friend may find issues is if/when her goes in for some sort of surgery. Doctors in general advise patients who are scheduled for surgery to lose weight first, and especially when the surgeries are non-life-threatening or cosmetic. I have known more than one transitioning person who was told they could not schedule “bottom” surgery until they lost weight.