Spousal support is usually based on one of two things. First, if your spouse “needs” support in order to maintain a similar lifestyle as they enjoyed during your marriage and second, if your spouse is entitled to support to “compensate” them for playing a role in the marriage which caused them to be less qualified to earn an income.
If your spouse remarries, then if their support is based on “need” there will be a greater effect on your required support payments then if it is based on “compensation”. This is because a new marriage does not provide compensation for a spouse’s inability to earn an income but a new spouse may be able to assist that same spouse with their lifestyle and “need”.