Probably the fairest way to do it would be to tell them that you will pay the charges, up to the current fixed rate amount, and everything above that is for them.
I know the company I use in Clare gives an allowance of 400 kg per 6 months, and charges/debits you per kg over/under. Perhaps you can suggest that they pay any overrun. The 400 kg is for non-recyclable material only, the recyclables are included "free" in service charge.
Note that in my case, the price per kg is 10c. That means that if I put out no rubbish for 6 months I will only be refunded Eur 40 from the Eur 400, so most is fixed cost. If yours is in same ball park, there should not be a huge overrun financially, unless there are 10 of them in the house.