Cheating or not??

So this is going to be a long post so bear with me.

My husband and I have been together for 13 years, since we were 16. We have been mostly happy and hes given me no reason to believe hes cheated on the past. We're very open about our feelings and have full access to each other's phones etc. Recently we've been having a rough patch cause I've put on a lot of weight and hes not very attracted to me anymore, we've been trying to conceive for 2 years now but only having sex once a month.

A few months ago he was doing a running race and got chatting to a woman at the start (hes very social and always chatting to random people so it didn't worry me) afterwards he asked if I minded him messaging her to ask how she went, I said ok. Turns out they've been messaging pretty much daily since then, I've read the messages, (without his knowledge) and there is nothing to imply anything more than a friendship but I have asked him twice not to message her anymore (in early dec) and with the rough patch we're going through I don't think it will help the situation. But hes still been messaging her and hes been the one starting the convo. I feel bad cause they're just talking about exercise and their weekends/days etc and the type of stuff that I'm not into but I feel like hes making a connection to her.

What should i do? Anyone else been on this situation? Or have any advice?