"Kerry and Thorne finalized their divorce in 1988... After Thorne requested an increase in alimony in 1995, Kerry sought an annulment of their marriage from the Catholic Church, a move observers saw as retaliatory. Kerry eventually received the annulment from the Boston diocese despite Thorne’s vehement objections." The marriage was formally annulled by the Roman Catholic Church in 1997.
Not sure if he was responsible to keep paying alimony after the marriage was annuled...
The church annuled it, not the state.
Totally separate matters. The alimony would have stemmed from the civil divorce, the annulment is a matter of the Church's recognition of the marriage. Without the annulment, they were still married in the eyes of the Church, despite the civil divorce.