At least the boyfriend is asking her, and not springing it on her when she visits. In any case he could be referring to anything - eg eating out with a mutual friend, going to a film, or anything. Maybe he has a child from a previous relationship that he sees at weekends, or a family member that visits. Just make sure you are around and available in case she ever wants to talk, but don’t ask other than beyond the usual “did you have a nice weekend, do anything special?” Type questions.
I think you need to buy your own laptop of tablet if you can afford it. If you can read her messages she can probably read yours. What if someone were to private message you about this thread?