I laud your devotion to accuracy, but I also offer some middle ground. Tobacco itself is known to possess psychoactive properties, and Middle-earth, insofar as it can be said to be a precursor to the modern world at all (for Tolkien himself drifted away from this idea later in his life and work), is eons in the past, when many things were heightened. So it's not so far a leap to imagine that pipeweed could have had as much in common with modern strains of marijuana as it did with what we call tobacco.

After all, our own tobacco originated in the Americas, probably somewhere in the region of modern Bolovia, and was not commonly used in Europe until the 16th Century. If one allows the conceit that Middle-earth represents a primordial version of modern Europe, then it follows that pipeweed itself also originated in the West (for was it not said to have been imported from Númenor, that land blessed by the Valar?). If indeed it was a strain of nicotiana, then it must have been of a varietal so pleasant to smoke that even the Valar themselves partook of it. At some point, it died out in the lands of Men, and was forgotten until its rediscovery by colonial exchanges with the indigenous people of the Americas.

TL;dr: Pipeweed is not weed, nor is it something modern people would recognize as garden variety tobacco. It's better than either of those things.