You need to read the book
Who Owns the Sky? The Struggle to Control Airspace from the Wright Brothers On Stuart Banner.
The primary issue was not conflict between states and the Federal government but between private landowners and the Federal government. Under the common law of the time, a person who owns the soil also owns the space indefinitely upward, "ad coelum or to the heavens". There had previously been successful lawsuits for trespass and/or nuisance for, among other things, bullets that passed over land without touching it.
Aviation in the early 20th century was largely unregulated in the United States, partially due to the issue of Federalism but primarily due to the question of if private citizens would be able to claim compensation for the government seizing their airspace. Neither state nor Federal governments wanted anything to do with it. The question was resolved in Europe before the First World War because national governments there were (largely) not federal, did not have the same sanctity of private property rights as the US and could see enormous national security issues in foreigners flying over your military installations, gathering intelligence about them and - as events ultimately showed - dropping bombs on them.
When the US finally decided that aviation needed regulation it passed the Air Commerce Act of 1926. There was never any issue about its constitutionality as the Federal government can rely on the Necessary and Proper Clause of Article 1, Section 8 which the Supreme Court has interpreted permissively since McCulloch v Maryland 17 U.S. (4 Wheat.) 316 (1819):
Let the end be legitimate, let it be within the scope of the Constitution, and all means which are appropriate, which are plainly adapted to that end, which are not prohibited, but consistent with the letter and spirit of the Constitution, are constitutional.
Basically, the Constitution is permissive in the powers it gives Congress - they have the power unless it says they don't.
The validity of the law with respect of the private property issue was settled in United States v. Causby, 328 U.S. 256 (1946) which overturned the common law that landholders owned airspace "to the heavens" but rejected that the government could seize it all down to ground level without compensation - in that particular case the government had to pay compensation for flights between 83 feet (the lowest that was made) and 365 feet (where the owner's property was deemed not affected by the flights).
The current state of the law is that you own as much airspace as is necessary for your current usage - this is higher in an office building in Manhatten than it is over a cornfield in Idaho.