How much should a non-custodial parent pay for child support with the following factors (and don't give me that "What ever's best for the kid" and "What does the other parent make?", I just want an amount):

1.) The non-custodial parent only gets to see the child every other week end
2.) The non-custodial parent isn't on the child's birth certificate
3.) The non-custodial parent makes a gross of about $700 per week

Assuming the non custodial parent is the dad, he really doesn't have to pay anything if there is no paternity established and his name isn't on the birth certificate.
How little or how much the non custodial parent sees the child has NOTHING to do with how much support to pay.
The court has to give an amount to pay until then the non custodial can pay whatever they want to. It is best to document and keep receipts how much they pay in the meantime so they aren't portrayed as a dead beat dad when they do go into court.

If I were you, I would make sure my attorney fought good and hard to make sure I was not paying for a child that may not be mine. Just because your name is not on the birth certificate does not mean you are not the Father.

DNA tells the tale. Then you can proceed. Child support is a percentage of your income, generally set by the court.