I think you should at least ask him to be exclusive with you. (Should have asked that the minute you had sex, really) If he won't be exclusive with you, then why would you want to be having sex with a man that could be doing other women while he does you too? If you think it's a burden now holding onto your own wants and needs without voicing/asking for what you want, wait as time goes by and you' find out he's with other women.
If you're letting him put himself in you then for all that is good, you should have the sense and confidence to ask that he not put it in anyone else. AND... if he won't give you what you want, then to have the self-respect and esteem enough to know that staying with someone who wants to share is not enough and you have the strength to walk away.
Geezzus H. Christ. Why are there so many women out there that don't respect themselves enough to look after their own emotional health? Surely you don't want him doing other women while doing you so why wouldn't you find out where his heart/head is at?
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion