It's clear that your friend would like to continue storing his possessions at the residence, but does not want to pay for internet service that he doesn't use. If your friend really doesn't sleep at or use the residence anymore, then I would say that's a reasonable request. He may very well be contributing to his girlfriend's rent or utility bills, and it may be breaking his budget to pay bills at two residences. Splitting the bills equally is really only fair if, on average, everyone is using the utilities equally.
For example, if one roommate is constantly running up the electricity bill by running power tools all the time, it would be reasonable for the other roommates to request that the electricity bill be split proportionally based on usage. If one roommate is running up the water bill by washing their car every day, it would be reasonable for the others to request that the water bill be split proportionally. If one roommate is constantly saturating the internet connection by torrenting (and seeding) movies and TV shows, it would be reasonable to request that they pay a higher proportion of the internet bill.
Your original agreement with your friend was based in part on the assumption that all three of you would be making similar use of each of the utilities, and you arranged for the utilities to be split in a way that was equitable and easy to manage. Since your friend no longer lives there, this assumption no longer holds true. Your friend is only occupying space at the residence, but is not using internet, electricity, water, etc. The key here is that your agreement was formed under the assumption that your friend would be living at the residence, and that is no longer the case.
In his view, he is being forced to subsidize your internet, electricity, and water usage, and he's right.
In your view, your friend is backing out of an agreement, and you're right.
The fact is, circumstances have changed. Your friend is not willing to pay an equal share of utility services that he isn't using. You want him to continue paying for utilities that he isn't using. These two positions aren't reconcilable. One or both of you are going to have to budge. Your question makes no mention of whether your friend wants to stop paying rent, so I'm operating under the assumption that he is still willing to pay his share of the rent. In essence, when you formed your agreement, your friend bet that he would be living at the residence for the duration of the lease, and that your utility usage and your girlfriend's utility usage would be comparable to his over that period of time. This turned out to be a bad bet, and now you're benefiting at his expense.
You have a few different options:
- Cut him out of the rental agreement, and find a new roommate. This will likely be the end of your friendship, and it may cost you in the form of higher rent until you can find a new roommate.
- Insist that he pay an equal share of the utility bills, despite the fact that he doesn't contribute to their usage. This will likely be the end of your friendship, and you risk having him sabotage your internet by simply cancelling the service or letting the bill lapse.
- Offer to compromise and allow him to pay some minimal flat rate towards utilities - it would cost some amount to keep the water hooked up and the climate controlled even if nobody were living there, and it would be reasonable for him to pay 1/3 of this amount.
- Grant him his request to stop contributing money to the utility bills and change the internet bill over to your name, with the understanding that if he goes back to living there, he will have to pay an equal share of the utilities again. Continue splitting rent 3 ways.
Which option you choose depends on how much you value your friendship. Even if there's a written agreement requiring him to pay his share of the utilities regardless of whether he's living at the residence, it wouldn't be prudent to insist on enforcing it if you want to preserve your friendship.
My advice: reevaluate your premise, and try to see things from his perspective. Then seek out a solution that is agreeable for both of you. I think you'll find that it's much easier to discuss this with your friend if you're offering to concede something rather than refusing to budge.