That is actually pretty easy to answer constitutionally speaking. If for example, we use the undue burden test such as the Supreme Court employed in Casey for abortion, it would be regulation that places an undue burden upon the individual's right of privacy. Thus, things like age limit restrictions, parental or spousal consent, even requiring abortions to be at licensed medical facilities could and have been considered an undue burden. Now, apply the undue burden standard to the 2nd which by the way is an actual enumerated right not found in penumbras and emanations.
If we look at the 4th Amendment, a simple case of infringment would be a search without a warrant and no probable cause. And so forth. The primary reason that the Framers had a Supreme Court is to A) defend the powers of the national government particularly from the states, B) avoid conflict between states, and C) referee conflicts among the branches of the federal government. What set the current constitutional regime was the post Civil War amendments which overturned Barron v. Baltimore and Dred Scott constitutional precedents among others. In particular, the 14th Amendment's due process clause through its fundamental freedoms extension has been interpreted so that in most cases among the states, attempts to treat state residents different than travelers, etc. on basic constitutional rights is well unconstitutional infringement by that particular state.
In addition, the privileges and immunities clause, although the Supreme Court's eviscerating dicta in Slaughterhouse, has still indicated that Americans have a fundamental right to travel etc. and thus things like two speed limits, one for residents, and one for non-residents or travelers would be held unconstitutional. In a related area, the dormant commerce clause jurisprudence limits state from enacting discriminatory legislation designed to favor state residents/companies. There were some cases involving weight limits on trucks in the 1980's where Arkansas and I believe Illinois had the older 73000 lb limit on trucks instead of 80,000 lbs, allegedly for safety of residents and damage to roads. These were struck down as hindering interstate commerce. Likewise, bans on out of state purchases of wine, despite the 21st amendment, in Michigan were struck down in Granholm v. Heald as discriminatory to out of state wineries.
For the present, the reason why NJ laws among others has survived is that the preceding Miller case still holds fascination for judges resisting the core findings of Heller. Miller, as well as the odious Cruikshank opinions have not been formally overruled but Heller read Miller as indicating that weapons commonly in use for individuals in the military and other purposes are protected by the 2nd Amendment and its purpose is to allow individuals who are not felons nor mentally ill to possess firearms for such things as militia service and self defense.
Heller goes lightly on the right to bear arms (aka carry) outside of the home as that was not part of the original question before the court. However, other court precedents, primarily in search and seizure does indicate that a person's car or perhaps RV has greater protection of the 4th Amendment than outside of that. Congruent with that understanding and many state laws that treat automobiles as an extension of the home, it can be argued that NJ is unconstitutionally impinging on the 2nd Amendment, the 14th's privileges and immunities clause (re right to travel), the commerce clause as Congress in FOPA foreclosed state laws contradicting it, perhaps if not directly the commerce clause then the dormant commerce clause and so on.