@Natalie634 If you charge the same price for one guest as for 2, then I would just ask him politely why he said his friend was only going to spend the night and has been there for a week. They are obviously using up more of your utilities, toilet papper, towels, etc. than 1 guest would, so in the future maybe you should add a $10/night fee for a second guest and make sure when guests book that they've entered the correct number of guests. Or make sure you're charging enough for 2 guests to stay for the same price as one.
It is a security issue for you to have an unregistered guest staying in your home- this other person isn't verified, you have no idea who they are and if they cause problems, Airbnb will not help you out, because they aren't on the booking. You should explain this to your guest, and you could alter his reservation to include the extra person, if you feel okay about that.
I would never have let a week go by without addressing this- as soon as you saw the other person was still staying there beyond the one night which you approved, you needed to address it head-on. Never be a push over or afraid to confront guests when they are pushing the boundaries or acting disrespectfully in fear of a bad review. Just be polite, but firm and professional. It's your home- you make the rules, not the guest.
The fact that your schedules mean you don't interact much shouldn't be a factor- these kinds of issues should be dealt with through Airbnb messaging, always, not verbal or phone calls or text, so Airbnb has a record of the conversation should things go south.
