Overweight w/ a period! Please no jokes or judging!

I'm an obese 19 year old and my period has just started to become normal again because im not stressed out too much but that's not my problem. When I'm on my cycle it seems as if because I'm big I always somehow leak out onto underwear or my pants. But with thin girls it seems as if they never have to worry about things like that. Is that maybe just an overreaction on my part or does all the extra skin cause that? What can i do to not be so anxious or nervous about it? Do thin girls really worry about that? Thanks(: