My girlfriend still thinks about her ex?

So I've been dating this girl for a few weeks and we like each other a lot or at least i hope so. About a month ago her previous bf that she had been dating for 10 months cheated on her and broke her heart but i feel like she misses her ex cause she still texts him even though she says she loves me with all her heart. I don't know whether to believe it and not think bad about it or be careful that she might just be using me. Also I'm not sure whether i should breakup with her because she might still like him and i might get hurt or just stay with her and hope she will get over her bf and end up liking me a lot more than her ex? Its either i should chill out cause weve only been dating for a few weeks and they were together for a long time so it might be understandable?? But i dont know...should i do something about this? please help me