He may try to be around you more, ask you questions about yourself, tell you that he likes a certain thing about you. If you want to hang out or do something, he will sometimes (if not all the time) make himself available. He might also give you strong eye contact and smile a lot; if he's really nervous, it'll come out in conversation when he doesn't know what to say. Shy and inexperienced guys might have trouble "flirting" and being "smooth", and he may be afraid of rejection, so don't expect him to tease you/kiss you/make bold statements of interest--those things may come only when he's SURE you like him and won't reject him. In fact, maybe you should make the first move (or the first few moves); to a shy guy, a crush showing him the ropes would be a dream come true.
As for your update question, some guys are definitely into girls who are a little overweight. Some of those guys might prefer the body type, while others overlook weight almost entirely and fall for the girl's personality--it does happen. However, I take "obese" to mean very/dangerously overweight, which may signal a potential health problem, and we're all attracted to healthy people. Everyone (both guys and girls) is also more attracted to those who take an active interest in improving themselves. If an obese girl makes an effort to take care of her health and return to a more normal-range weight, she'll definitely get more attention.