Need Advice.. Another Woman & A Lie

My bf and I have been together for 4 years. We've lived together for over a year. A year into our relationship I found texts to a woman named Kelly. They seemed innocent enough. Back and forth conversations about hanging out but it seemed like it was usually a group hang out. I talked to him about it, and he said she bugs him all the time and he deleted her number. At this point, he also started locking his phone. A year ago I noticed a Snapchat notification from Kelly on his phone. I asked him to unlock it so I could see if it was just a one time snap from her randomly or if they had talked a lot (Snapchat puts emojis next to friends names to signify how often you talk to them). He got really defensive and started putting me down for my trust issues. I went to smoke and when I went back in, he said "here ya go." and gave me his phone. he had deleted everything. Facebook, Snapchat, everything. he said she snaps him, but he never snaps her back. I gave up with the conversation. Last week I went through his phone (I watched him put the password in one day and remembered it) he had reinstalled Snapchat and Kelly was his only contact. the emoji by her name meant they talk on and off all the time. so he lied to me when he said he never snaps her back, because the last snap was from him to her sent the day before I looked through his phone. anyway, I'm going to talk to him when he gets home on friday (he's away at a conference for work) I just don't know how to go about it in a way where we can actually finally put this issue to rest for good instead of sweeping it back under the rug. I believe Kelly is more than just a friend. he has other female friends and I know how they met, where they work, and we've hung out with them in person. he never talks about Kelly. I know nothing about her and he goes out of his way to hide her from me. any advice would be greatly appreciated. I don't want our relationship to end, but I don't know what to do anymore.