what should i do? did my bf betray me?

dear readers, i hope to seek some advices from u guys as i'm heart broken n duno wad should do lately.

i have been with my bf since last 3 years, we:upset: have been together with conflicts,arguments n of coz there were sweet moments as well.
lately, we have been quarrel alot. & he is having some stress from work i supposed. n we quarrel again lately. i did quarrel with him about his female colleagues at work.
n now i realized he trying to look for 'sex mate' online. n he told that this was because we quarrel too much n he is too stress. he said after he searched n searched, he close the website oredi as he know he is doing something inappropriate.

now he said he really love me deeply n wish to be with me forever (marry me).
i have proposed to break up with him, but he seemed to be strongly wish to hold on this relationship.
so i continue to stay with him, but i'm started to feel insecure as i scare when will him have that thought again?

what you guys think? without time, how to prove a guy truly love a girl in a fast pace? as we are girls, girls' youth is limited.