If I understand what you wrote, basically you'd honor your visit rate ($15 each=$30 for 2) which he was fine with, and charge $10 more for staying overnight. The rates sound fair, but I would not suggest it. Here's why:
If staying overnight is a service of value to the friend, I could see offering it for slightly more because staying over would be committing to care for only his pet (no other Rover pet business) during that time frame. Then again, you mentioned that you'd leave after 10 AM and return by 7 PM, which frees you up to do other walks, visits, etc. Since house sitting is generally providing 24 hour/day care, unless there are other factors which indicate the friend wants their house watched, I probably would not suggest it, especially since it sounds like the dog is fine by itself.
In consideration of a long term relationship that matters, if you don't have other commitments, I could also see offering to stay over for no additional charge, as that saves you the drive back and forth a couple times a day.