I’m not a rocket surgeon or anything, but I’m guessing he’s willling to pay for it because you can’t afford it and he can. If he was THAT focused on you hitting the gym to get yourself together (whatever that means, I haven’t seen you) then he’d not only offer to pay for the full thing he’d make sure he took you there himself.
It’s possible that your boyfriend actually really really loves you and just wants to help you out in your moment of need. I’m guessing you told him that you wanted to go to the gym but couldn’t afford it and because he’s supportive, he offered to cough up the other half. And here you are writing in questioning his motives.
So sad. So sad.
If anything you might want to ask him to perhaps make it a couple activity with the two of you all so that you all can enjoy the hard work together or something. I don’t know. Anything but questioning the dude.