He’s still keeping tabs on his ex! Would you still stay with him?

It’s almost a year my boyfriend and I been together. Couple months ago we broke up because he cheated on me with his ex-girlfriend that dumped him over a year ago ... Our agreement was for him to block her and part ways. Come to find out while we were inside watching movies I glanced over to his phone quick and saw him watching her social media stories with his brightness down. I could still tell by the username and avi who it was; the ex. I didn’t say a word, just went to check if he’s following her.

They are both not following each other so he unblocked her and he’s sneaking around on her social media. It’s been over a year since they have dated. He is a amazing guy and chose me first but I’m having second thoughts.