Life is not fair, and the sooner your daughter learns that, the happier she will be in life.
Are you afraid she won't like you as much if you don't give her as big an allowance as her father does?
When my daughter turned 10, I started giving her an allowance. It was enough to cover her student bus pass, her lunch money, her supplies for her pet hamster, and a bit of pocket money for fun.
She learned how to handle money and now in her 40's has never had trouble with having too much debt, nor with impulsive spending.
Allowance is SUPPOSED to be a training program, not a self-indulgent let's-learn-how-to-blow-my-money experience.
Just what does she have to pay out of this $15 a week she's being given? Anything? if she is being provided for, there is no need for allowance. And if she is old enough, let her babysit, and mow lawns (or shovel sidewalks) for the money she WANTS.
This is how you raise a child to become a self-sufficient honest person.