It really depends on your needs and desires. Does this appeal to you? Do you want/need longer bookings? Personally, I find 3 - 4 nights the best. By then I’m ready for guests, even those that are wonderful, to move on down the road. Hec, I’m ready for my sister to go by that point, too - and I love her!
Do you want this person to repeat? I’d be concerned that, after awhile, they’d get on your nerves and then it’s awkward to tell them to stop coming.
But I would not, would not, reduce your rate for them, unless they really are awesome and it’s worth it to you to know you have the income coming in. Otherwise you’re tied up making less than what the room is worth, right?
If, however, you think you enjoy this person and they are respectful, and you prefer to have ‘easy money’ then longer bookings, go for it.
But I would make it on a provisional basis, set up specific times to sit down and talk about how the arrangement is going, so you can talk out any small problems before they morph.