Sam Winchester has big body image issues. As anyone who watches the show for a while can see he carries himself as someone who doesn't feel comfortable. He's often hunched over and wears excessive amounts of clothing. His standard dress when out in public and interacting with other people is an undershirt, a t-shirt, an overshirt and a jacket. But when Sam is around Dean primarily, alone with him or sometimes in a public setting but only interacting with him, his layers are cut down to an undershirt and overshirt.
It's because Dean is his big brother and he trusts Dean not to make fun of him for the things he's actually sensitive about. In his own words in the Pilot he states that "Sammy was a chubby twelve-year-old" and I think he still sees himself like that. Especially because he is a big boy; he's very broad, very tall and he takes up a large amount of space. When he's with Dean is nearly the only time he wears minimal layers and stands up straight. He feels safe with Dean, he can be himself around him.
It's worth pointing out that there are only two other people Sam has ever been seen wearing less than three layers around. Jess, who he loved and trusted enough to live with, and Madison, who he was hot for and had sex with. Now, this doesn't necessarily have wincestuous connotations; what it reaffirms is that Sam trusts Dean more than anyone else in the world.
Madison doesn't not count as largely in this argument because while he was in minimal clothing around her it was for sexual purposes. And while it is possible to have sex with multiple shirts on it is not as aesthetically pleasing, especially on a visual medium such as television. Jess counts twice as much to make up for it though. Sam trusted her enough to live with her. Not only was he comfortable enough to share a bed with her and wear a single t-shirt in their bed and her presence but she was comfortable enough with him to wear an old shirt and mis-matching boyshorts to bed with him.
In fact, in season one the Pilot and that first scene with Jess and Dean was one of only two times that season Sam wore only one layer (the other being alone in the motel room with Dean in Something Wicked). In Hell House he wore no layers, just a towel, and only in the room with Dean right there.
In season two the only times Sam wears a single shirt is in Everybody Loves a Clown when confronting Dean about their father's death in a very emotional scene (I'm sure I don't have to explain the trust there), in Playthings in front of Dean while he is throwing up (another sign of trust, as people tend try not to vomit in front of random people if they can help it and Sam kept the bathroom door wide open even in between pukings just so he could talk to Dean) and in Heart after Madison takes off in his overshirt and Dean comes to try and rescue him.
Dean's layers do not count in this observation/meta/essay because he has a standard of wear. He wears a t-shirt, an open button-down over it and a jacket. The only changes in this are the rare occasion when he forgoes a jacket and the equally rare occasion when he wear a Henley instead of his favored t-shirt/button-down combo. Dean, very obviously, doesn't have the body image issues that Sam does.