With all of the planets Earth is now in contact with it shouldn't come as a surprise to the crew that not all of its inhabitants are fully human anymore. Leo has dealt with stares all of his life but mostly they are to do with the realisation that he is one of 'them', more of an 'Oh...right moment for people to process and somehow that makes the disbelief of the students at the Academy so much harder to deal with. They are just wings after all, and these are not backward farmers and old women that like to gossip but Cadets that should know better than to judge him. It wasn't even about the wings, really, because he'd seen plenty of them around at the Academy but that he was human and he had them. It wouldn't be such a big deal if his skin was purple or he had extra limbs to go with them. He had wings and nothing else that made him any different from Jim or Uhura or any of the others and that seemed to freak people out.
Huge changes they could deal with, but small ones just seemed strange in their eyes. It was as if they thought Leo's wings were some sort of dangerous mistake. For fuck's sake, they didn't even do anything and that is probably why it all gets to Leo so much. They are not strong enough for him to fly or even hover and he can't do any 21st century sci-fi movie shit like pin people to walls with them or pierce through their hearts. No, they just sit there and for the most part get in his way unless he tapes them to his back which is uncomfortable, time consuming and in general just a pain in the ass.
One of the big reasons Leo puts up with Jim's bullshit is because the kid knew him before he knew he had wings and when he found out he just blinked, nodded and asked if there were any adjustments needed to their room. As a Doctor, Leo knew some beings felt their wings react badly to certain temperatures and appreciated the concern as opposed to the disbelief, 20 questions and suspicion. The little shit had tried to pet them a few times when drunk off his ass but Jim did a lot of weird stuff when drunk and Leo could let it all slide because he'd also broke some guy's jaw for trying to do the same thing.
The wings are not a big deal but that doesn't mean Leo wants some stranger's dirty paws all over them either. Others are not so nice about things and many don't attempt to touch him physically but give him verbal slaps to the face. Most have to do with his mother but Leo is a grown ass man and he will be damned if he gets into a fistfight over the damn things. Besides, Jim seems happy enough to do that for him. Every bloodied knuckle that he has to tape for him convinces him that the guy is one to keep around and stick with. He is a grown ass man able to defend himself but Jim steps in anyway, takes offence anyway, and defends him not because he needs to but because he is Leo's friend and he wants to.
All that is why when a mission goes wrong years later on the Enterprise and Leo takes a laser to his left wing, Jim is the only person he gives permission to touch them and repair the membrane. The rest get threatened with everything under the sun and he screams the hospital wing down until the nurses clear off, most giving him unimpressed looks and mumbling about protocol and Jim's lack of training. Leo could not give a rat's arse about any of that. He is the Chief Medical Officer and if he says Jim is perfectly capable of rubbing some cream on his wing and taping him up then he is.
Everyone else will want to poke and prod more than they need to. They will want to write down notes later and ask questions that Leo doesn't want to answer. They will treat his wings like a science experiment and not just the part of Leo that they are. They don't do anything and it isn't like he has passed them down to Jo. He just happens to have wings and in this day and age, that really shouldn't be as much of a deal as it is for some. No, Jim will just do his job and leave him. He's the only person he trusts with his wings. Hell, for a long time Jim has plain been the only person he trusts period.