After Responder makes a 1-Over-1 bid, Opener can raise with only 3-card support when he does not have anything better to bid.
If Responder is weak (<10 HCPs) and has only 4 cards in his suit, he just passes and may be playing a 4-3 fit (although more often, opener will have 4 cards for his raise).
If Responder has enough points to bid again (a good 10+ HCPs) and he has only 4 cards in his suit, he should usually bid 2N over the raise to show that he only has 4. This is invitational, and opener may pass 2N, raise to 3N, or bid another suit -- whichever his hand dictates.
Here are examples of hands with which opener might raise with 3-card support after 1-P-1-P: