A stepparent adoption usually requires that the parent whose relationship and rights are being terminated consent to the adoption. Usually the parent must sign a document consenting to the adoption, and usually the parent has a "window" of time in which to void that document, or the custodial parent has a time period in which to bring the adoption action before the court. In some states, the document may not be revoked once it's signed by the parent.
If the parent won't sign the document, a court will need to approve the termination of the parent's relationship and rights. This may not even be possible in some states, depending on state law.
Even when a parent has consented, a court will need to find the adoption to be in the child's best interest. The factors the court will look at vary by state law. The stability of the custodial parent's marriage is one factor, and courts generally will not allow an adoption into a brand new marriage.
The adoption will normally terminate almost all ties that the parent has to the child, and provide those ties to the adoptive parent. These ties include rights to custody and visitation, the obligation to provide support, and, frequently, inheritance rights of the child and the adults.
Many states require that a child of a certain age - usually in their teens - also consent to the adoption.
The adoption terminates the legal relationship between the parent and the child, and creates a legal relationship between the adoptive parent and the child. It is that relationship which is the source of the obligation to pay support.
It's possible the parents of the child may allow contact; it's possible they will not. If they do not want any contact and you are persisting, you may be violating the law.
Because adoption law and grandparent rights law is almost entirely state law, you really should consult with an attorney in the relevant state.