Do allergy shots cause body weight changes?

No. Some older allegy medicines increase appetite. In fact Cyproheptadine has been used to help underweight kids. Allergy shots dont do this at all.
No. Allergy shots don't have calories nor increase a person's appetite, so do not cause weight gain. However, if the shots worked well and a person got rid of his stuffed up nose, sneezing, watery eyes, or other bothersome symptoms, then the person would be happier and feeling a lot better. Then, he might develop a bigger appetite, go out more often, and end up eating more calories and gaining weight.