Question: if a two cent tax on newspapers and requiring an ultrasound before abortions are deemed unconstitutional infringements on rights, what about everything required for guns?

In 1936, the Supreme Court struck down a two percent tax on newspapers as "unconstitutional under the due process of law clause because it abridges the freedom of the press" (Grosjean v. American Press Co., Inc.).
For abortions, requiring an ultrasound before an abortion is deemed to impose to great of a burden on those seeking an abortion.  The Supreme Court just turned down an appeal from the state of Oklahoma on this issue.

The rejected Ultrasound Act stipulated that at least one hour before an abortion physicians must 1). perform an ultrasound 2). explain what it depicts 3). show the pregnant woman 4). provide a medical description “which shall include the dimensions of the embryo or fetus, the presence of cardiac activity...the presence of external members and internal organs….”

Interestingly, ultrasounds are generally promoted as being simple for women.  During the "first trimester fetal ultrasound typically takes between 15 and 20 minutes" and during the "second trimester ultrasound, completed between 18 and 22 weeks, is usually the longest procedure, lasting 30 to 45 minutes."  The typical cost of an ultrasound is "around $200."

So, are a woman's reproductive rights greater than a woman's right to her own life?

Yet, in Washington, DC it takes 5 hours of training to get a license and register a gun.  One must also take a 20-question exam on DC's firearms laws and regulations.  You must also give your fingerprints and submit a pre-owned firearm for ballistics testing at the office.  Additional cost include having to take the forms in in person.  The total dollar cost is over $500.

Alito in Chicago v. McDonald: "In sum, it is clear that the Framers and ratifiers of the Fourteenth Amendment counted the right to keep and bear arms among those fundamental rights necessary to our system of ordered liberty."  Scalia in Heller also referred to these rights as "fundamental."

Bottom line: How can a 20 minute test that costs $200 be deemed of as imposing an undue burden on a right, but a 5 hour training requirement and many hours of filing out forms and delivering them plus over $500 in fees not be considered such a burden?  How can a 2 percent tax on newspaper be deemed abridging the First amendment but what could easily be over a 100 percent tax on a gun be viewed as OK?

The court in Grosjean v. American Press Co., Inc. struck down the newspaper tax because it was reducing circulation of what it deemed to be a "fundamental right" ("it is seen to be a deliberate and calculated device in the guise of a tax to limit the circulation of information to which the public is entitled in virtue of the constitutional guaranties").  The tax on gun and ammunition purchases would seem to have the exact same effect on guns.