I don't have the extreme need that many others on the spectrum have for weighted blankets, but a heavier blanket does make me feel better. I have a nice, weighty comforter that I use with blankets. However, in warm weather, it's not possible for me to use it. I use several industrial fans instead of the A/C, which kept breaking down. The fans work good, but I still won't use the comforter while running the fans. Industrial fans are a lot cheaper to run than the A/C, and don't keep breaking down. If you have enough of them around the house, they can do a good job. I have three industrial fans, in different rooms, plus the overhead kitchen fan/light. I will sometimes use one blanket with one of the fans, if it is cool, but I expect it to warm up before I wake up. I have an irregular sleep/wake pattern due to several health issues, so I go to sleep and wake at any hour of the day/night. I do like having a blanket on, but in the heat and humidity we've been having, I've had to mostly do without.
Perhaps this comfort/security feeling with blankets is a hold over from when we were enclosed in the womb. Many people on the spectrum may have a need to continue this safe, comfortable, enclosed feeling when resting or stressed. I am fortunate that my need for this is not overwhelming. I am able to sleep without a blanket when it is too hot for one, but it does feel better to have one on.
There is no harm in using a weighted blanket, as long as it's not too heavy or too confining for the size of the person using it. This is something harmless that can help people rest better and de-stress, too, so if you think your son would benefit from it, go for it. From what you described, it sounds like he may like a weighted blankie.