You’re “required” to register it in the state of primary use... sounds like NJ would be the correct answer. Gtstricky is alluding to the fact that Delaware does not collect tax, but I’m assuming you’ve already paid sales tax on the boat
in PA. NJ will want to see proof of tax payment otherwise they will want to charge you sales tax (use tax?) I’m not an accountant, so check with your accountant about that. Each state has different requirements;
“Boats and marine equipment
which need not be registered:
Those not based in New Jersey or operating here less than 180 consecutive days
that are operating under a federally-approved numbering system from another state”
(Emphasis is mine)
Hope this helps.