Q. Should my company withhold my New Jersey state income tax for every pay check?
A. No. But, it's not unreasonable for them to do so, in your situation. Ideally, they should only withhold for the pay periods, you actually work in NJ. But that may be expecting too much from them. You might try adjusting your NJ-W4 to the minimum withholding.
https://www.state.nj.us/treasury/taxation/pdf/current/njw4.pdf
