Is it weird that my boyfriend constantly texts another girl?

My boyfriend has been texting a girl from his classes that he met maybe a couple of months ago. I would say texting other girls is okay, except they've been texting each other all day for almost a whole week. I can see this constant texting continuing as well. To my knowledge, there is no flirting in the texting. The girl usually initiates the texting, but then the texting goes on the whole day sometimes until 2 or 3 AM. My boyfriend has never really been addicted to texting before which is why the behavior seems so weird to me. I told my boyfriend I feel weird about this amount of texting and he just turns it around on me and says I'm not letting him have any friends. This is so not the case, because I don't think you need to text people ALL DAY in order to have friends. He says they are just friends and he is not interested in her, and I want to trust this so much but I just have this feeling that I can't. The girl also constantly asks him if his girlfriend is okay with them hanging out every time they do something together (study or get something to eat). I find this odd because she has never tried to get to know me, and she still texted him constantly when she knew my boyfriend and I were fighting over them hanging out and texting. If she was actually concerned you'd think she would've at least lessened the amount of texting during that time.
Is it weird that my boyfriend constantly texts another girl?
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