The series itself was sometimes inconsistent on this fact (as well as other things about how leaping works), and there was no answer given in the show itself to my knowledge, so any answer is likely to be speculative at best.
Although the canonicity is not the best, it is addressed briefly in the Quantum Leap comic, issue #12, "Waiting" (in which Sam leaps into a recluse who operates a gas station in the middle of nowhere, waiting for someone to come along who's life he's affecting, and he and Al just talk).
Al: Remember what I said? Paradoxes don't matter in the real world. Here's something else for you to chew on...
Al: Why is it that whenever you leap into somebody's place, their clothes always seem to fit you? You've been petite women and even children, but you can still wear their clothes.
Sam: Gee, you know, I never thought about that...
Al: It's not something you would normally think about. You just wear the clothes and don't notice that they fit, even if they are tight or loose sometimes. Look at what you're wearing now. Lucky is a scrawny little guy, barely four and a half feet tall, but the clothes are on you and they're not torn to shreds!
Sam: So... do you have any ideas about this one, Professor Calavicci?
Al: I confess that one had me stumped. But Gooshie came up with a possible answer.
Sam: Gooshie!?
Al: Yeah, the little guy with the bad breath who--
Sam: I remember who Gooshie is, I just don't remember him ever coming up with an answer to anything before.
Al: This actually almost makes sense. Gooshie figures that the leap causes a disturbance in the molecular structure of the clothes, making them unstable, so that they can stretch or shrink to fit you.
Sam: Clothes made of unstable molecules?
Al: Maybe.
Sam: Gooshie reads too many comic books.
Al: Probably.
Sam: But, wait a minute.
Sam: I had to take off the boots right after I leaped in here because they were too tight. Why would that have happened?
Al: Uhhh... maybe they were too tight for "Lucky" before you got here, but he was just used to it. I don't know.
Al: Anyway, it just proves that there is a whole lot about your quantum leaping that we still don't understand... things we can't account for...
But that's not really an answer either. I'm unaware of any official (albeit again, possibly non-canon) attempt to answer in any other media.
Fans always come up with their own theories, of course, and, for me, the best fanwank answer I've read was that Sam's body is somehow "mapped" into the space the original person would occupy, like say, imagine a stretchy balloon with Sam's face on it could be filled with a different amount of air and shoved into a set of clothes of somebody else, but a far more complex three-dimensional balloon of his entire body.
