Why do I owe on my PA tax return and get money back on my Delaware tax return if I work in Delaware and pay 6.6% and in PA the tax bracket is 3.07% ??

It sounds like your employer is withholding taxes only in Delaware.

Since you work in one state but live in another, you are required to pay taxes to both.  You do receive credit for the taxes paid to Delaware on your Pennsylvania tax return, but if your employer didn't withhold taxes for Pennsylvania, this is why you see a balance due.  

You may have done your state returns in the wrong sequence.

Be sure you completed your non-resident DE return before you did your home state PA return.  In TurboTax the "other state credit" will not flow properly unless you do the returns in the correct sequence.