Will the courts take into consideration that I inherited most of the debt from our marriage when calculating the new child support amount?
Generally, the court will stick to the child support guidelines in recalculating child support. There are some factors that may be considered at the discretion of the court that may justify a downward deviation from the guidelines.
In your case, you would most certainly make the argument that through equitable distribution, you were assigned the majority of the marital debt and this should be considered in the determination of child support.
There are several other factors that would adjust an analysis. For example, how much parenting time do you have with your child and what kind of direct contributions are you making towards the child.
If your income has increased and you do not have to go for a review, I would let opposing party file a modification. A review of your divorce decree would be necessary to see if this is a mandatory review and whether your liability for marital debts was factored into the decision.
I cannot give you specific legal advice as I am not familiar with the facts of your case. For a more in-depth answer, please consult a family law attorney in your jurisdiction.