Clairvoyance and Clothing Optional
Billy has the power of clairvoyance which is basically a second sight. He was scouted by Dr. Azuma for his sharp shooting abilities. Dr. Azuma recognized Billy's ability right away and recruited him into A-Team. Billy can see things outside of the ordinary realm of vision. His ability is not excluded to seeing things that are not there. He uses his powers to see inside of things from the outside. He uses this power to check on hostages, map places, and get a feel for entry and exit points (and if he so chooses through clothing). I believe he also uses it in his shooting in a way that prevents him from ever missing a shot. His eyes glow mysteriously when he uses his ability. In addition, Soh states that Billy's power is enhanced whenever he has a gun in his hands. I think this has partly to do with it being something that Billy trusts. It's gotten him what he needs in his life and so he feels confident and more relaxed. I feel like that would make his concentration while using his ability much clearer and sharper.
He explains that his powers of clairvoyance help him with his shot and seeing into buildings, making maps, and scouting places out. This is particularly useful for infiltration as it lets him see how many people are in an area, the hidden passages, and allows him to hit anything that comes his way. The downside is that as he uses this power it causes his body to get too hot. (The science here makes sense, use of energy produces heat, so essentially he overheats his body when he uses his powers.) We quickly find out he has a few defining opinions. One, women are awesome. Two, clothing is optional. After something like two days of living with him, he thought you'd be used to his assertions.
But don't worry! Billy is not just some jerk who likes embarassing you. He does everything in his power to reassure you. Actually, he does enjoy teasing quite a bit. Besides, that, because it's his place, I'm not sure that we really have a reason to complain about the way he dresses. (Would we? Really?) Although his initial reason is because he's muscly and so his body temperature is high. Another reason that Billy believes clothes are optional is because it's humid in Japan and it makes it too hot. If he lived in Texas before, the change in humidity would be tremendous, so I can see why he would be trying to keep cool. He also invites his charge to remove her clothes, because he can see through her clothes if he chose to use his clairvoyance. However, that's not the point of "being naked". He could do that any time, for him, lacking clothes is also part of a freedom that he enjoys. He finds it liberating and thinks everyone should partake.
Basically he's good looking, he's cool, he's an unrivaled shot - and he knows it. His clairvoyance helps keep him there. I don't know that his ability is really enough to keep him half dressed, it makes sense as to why it might, but mostly, I think he's just proud of the man he is and has found a pretty easy excuse to throw around (always a well aimed shot, if you know what I mean).