My LO has slept with a blanket since approx. 2 months. I just tucked it into the sides of the mattress. I also dress her in anything comfy. Shorts & tee, pants and long sleeve tee or footed pj's. She doesn't know how to cover herself yet but she seems to do ok.
For those moms looking for good light weight footed pj's Carter's has them in almost all sizes. My daughter has 2T ones and I know there are 3T & 4T too. If you go to the one at Spectrum you'll usually find them on sale too.