Step Accross so he's like horizontal to you. I had a lad at my gym who did this and once i learnt the step accross Im always knocking him down because there off balance once you hit them and you've stepped accross, its impossible to stay leaned (which he will be) and rotate your WHOLE body properly.
You could use the double right hand, one to the body, one up top. You could double jab your way in to set up a body attack. You could duck and then come up with a left hook. But personally, I think jab, to get their head back, and right hooks to the body works very effectively, as long as you stay away from their right hand power. And you could also step to the side and come with a straight right hand when you got them off balance. It just depends on how fast they are and how fast you are and if you can get them stuck.
Mayweather is doing the samething, but we can not compare Mayweather with your guy at the gym. But what you have to do is, find angles to hit him with your jab, so jab low and jab to his chest, jab to his head, until he leaves and opening for you to throw the right hand and the second thing you can do is to try not to throw your hand long, so just pretend you are punching him with a hook or a jab but turn it in a different punch, so confuse him. and try to time him, because if he is not that good, he has 9 out 10 time the same move and the same 2 or 3 combination he is throwing before leaning back. I hope this helps you a bit.