I'll tackle this firstly from a mathematical viewpoint, and then from a legal one.
You're present for 7 nights per week, while your colleague is present for 4 nights. That means that there are 11 'person-nights' involved, four of which relate to your colleague. Therefore he should pay 4 elevenths of the bills. That's about 36.4%. However, that might be a bit high because you're also using the utility services during the day (as well as the evenings and mornings) at weekends, when he is not. So it would seem more reasonable to charge him around 30% (or, at the most, one third) of the bills.
Your question about whether you can back-date the bills could keep teams of lawyers busy for months ;-) Your lawyers would argue that your initial discussions represented a legal contract, thus giving you the right to bill your colleague for utility charges since February. His lawyers would argue that you'd told him how much he owed you each month and that each payment was a separate contract. Since he'd paid the full amount demanded at the time, they would say that he had completed his contractual obligation and you have no right to demand further payments.
I suggest that you should remind your colleague of the original agreement, and levy charges of around 30% of the utility bills from now, but write-off any charges relating to previous months.
Chris