Spending the weekend with her might be completely innocent, but it looks bad. Can't a man have female friends? Of course he can.
I decided not to be the jealous girlfriend, and I was fairly convinced that she just saw him as a close friend, but it turned out to be either an emotional affair or a full blown affair - EA probably. He had a massive crush on her.
We parted not in the slightest bit amicably. The lies he had told me meant that of the many years we'd been a couple, I had no idea of what had been really going on. Was I second best? Or second best after she became single. It nearly cracked me up.
The X treated me brilliantly a lot of the time - things were going a bit downhill for about a year before I found out. It took at least a year to get over it.
When I posted (in despair) on here, I got the "Have you no boundaries?" posts. I did have boundaries. I had told him that I found his spending time with her inappropriate and so on. He had reassured me that there was nothing going on. My gut feeling knew that she would split us up, and in hindsight I should have walked away at that first time my gut told me but I loved him (not really, I loved the man I thought he was) and he was seemingly nice to me.
You are not me, and your situation isn't necessarily the same.
You can either meet her with him so you can see how he is when she is around or you can walk away.
If he refuses to let you meet her, walk away.
Hope that helps.