Everybody is different and this is a sensitive topic, I'm 26 and can remember it quite clearly, I did grow up quite quickly though and was out on my own by the time I was 17.
I went to a good catholic school and there was a whole range of people there by the time we left at 16, from the girls with steady boyfriends, to the girls who hadn't even really realised about boys/girls yet. So a lot of it depends on the maturity of your son and his girlfriend.
I took it to mean 5 weeks + some additional weeks (as stated in the OP, that he'd been nagging from five weeks), so I was thinking along the 3 months line
Which isn't a casual fling really, and when things start to settle down no matter what age you're at.
I agree that many people wouldn't have snuck off at 17 but some people would. For space if nothing else. Time alone to watch DVDs and be intimate but not THAT intimate. I think that her spending more time at your house is a good idea generally, and also that they have alone time.
But I also think If he's asking to have her stay then the likelihood is he's already thinking/is involved with her in a physical way or confident that that's where this relationship is heading, and if that's true then they'll likely find a way around any rules
That might be from personal bias!
I would also say, if he's 17, how long before he goes to university, lives in halls and does whatever he wants? Maybe teaching him responsibility now would be beneficial.