Is child support based on anything other than the parents’ incomes?

Yes. The child support computation also takes into account the following:
Other children living with a parent
Child support ordered for other children
Spousal support paid to any former spouse
Amount of local income taxes paid
Mandatory work-related deductions
Child care expenses that are work-related, employment training-related, or education-related
Cost of providing health insurance for the children
Non-means-tested benefits, including social security and veterans’ benefits, paid to and received by a child or a person on behalf of the child due to death, disability, or retirement of the parent