Wearing a hat... bar mitzvah or marriage?

I have heard from some older people that in some pre-war German communities men did not start wearing a hat until they were married and not at bar mitzvah like they do today.
And even those communities where boys did wear a hat once bar mitzvah age they certainly did not start at the same time they started wearing tefilin shortly before bar mitzvah, but waited until they were actually bar mitzvah.
Anyone care to comment?

David