Why is it that most Ashkenazim that are not married do not put the Talis over their head?
The minhag is sourced to the Talmud (Kiddushin 29b) that only married men would put the talis over their heads.
א"ל מאי טעמא לא פריסת סודרא א"ל דלא נסיבנא
דלא פריס סודר - כדרך הנשואין שהיו רגילין לכסות ראשן
so that woman who are looking to get married may see who is and is not married.