What is the percentage of taxes that should be taken out of your weekly pay if you work out of the state of nj but live in nj

You must report your income to both the states.

If you are present in a state, then any income earned during this period, must be reported to the state.

To your resident state, you must report your worldwide income for the year. Read: Your U.S. Tax Return: Working or Living in Two or More states

It depends in which state you work.

If you work in New York, then have NO taxes withheld for New Jersey if your salary is your only income, because the tax credit offered by New Jersey for the NY statxes paid will completely offset any NJ tax liability.