Although Aaron answered you question re how to confirm paternity by DNA. If you don't have access to the child for a private test, you will need to file a petition with the ocurt to establish paternity, then the court will order a DNA test which is more expensive than the private test, those results in turn will help you decide what to do next, if you are not the bio dad, you will want to file to disestablish paternity and any assocated child support orders that signing the AOP may have envoked. If it is your child you may want to file for some sort of custody and visitation and expect that you will be ordered to pay for child support from the date you signed the AOP and if mom and or child are on state aid, that the state will also seek money from you. YOur actual name on the birth certificate is the least of your worries.
As to the weight of the child, that is right on target for a child born at 36-38 weeks and not unusual for a 1st child to be born premature. Remember children have 2 sets of potential chromosomes, so a baby's features would not necessiarly be exactly like yours as a baby, unless she was your sister and shared the same gene pool.

