Regardless if the baby is sleeping or not, the pay (especially for weekend evenings) should be in the $10 an hour and UP - range. If you have some 13/14 year old come and "house sit" with your child there...then you can probably get away with giving them around $5-$8 an hour.
I babysit during the day, as a "job", and it doesn't make a difference if the child is sleeping or awake, the rate does not change. Having the child nap properly is actually a PART of the job!
I do charge $8 for babies and $10 for them as they reach their first birthday with me. But that is week day babysitting and a lot of "baby" naps included. It is also in my house, so it gives me some time to do my things while they sleep, versus being away from my house babysitting. That is why I charge a little less. (because I get to be home)
I know it makes that "movie night" difficult when you have to pay a sitter....but if you hire someone to give up their weekend evening to "sit" at YOUR house...pay should be at least $10 an hour.