I know of some nannies who actually charge more money when they babysit on nights and weekends because their nights and weekends are more valuable to them.
I am actually one of the PPs who recommended that the OP lower her rate or offer to do fun activities with the child for free.
But in a way I can understand the nannies who charge more for nights and weekends. I have to agree that my nights and weekends are much more valuable to me than my weekdays. If MB were to ask me to switch some of my daytime hours for a late evening or weekend I would not be too happy about the situation. Admittedly, I would probably do it anyways because my bosses are wonderful and I really like to be flexible with them but my evenings and weekends is time that I spend with my family and I find that much more valuable than my weekdays.