Bilbo

Legolas -- Snow Trolls are mentioned briefly in the Appendices of Lord of the Rings, in the story concerning Helm Hammerhand.

Gwaihir -- Not only is there Letter 153 which is against your opinion, but there is also a logical reason supporting the 'multiple origin' theory. I proposed that the Trolls had originated through two different methods. One was that the Trolls were pre-existing creatures, which were 'tinkered' with by Melkor, and thus bent to serve him. The other way was the creation of an outer body (like that of Aulë's dwarves), which were then animated with the spirit of the boldogs (like the dragons were animated). However, your arguement against this is that all the Trolls are essentially the same, and therefore they cannot be derived from different sources. The way in which I presented the origins, though, can indeed make it possible for the Trolls to be descended from differentiating sources, and still be nearly all alike. This scenario is one I find very likely: Melkor could have stumbled across this 'primitive race' of Trolls (whose probable origin I will address later), and bent them to his will, and thus inflated his servants. However, he found that this race was not numerous enough to serve him effectively. Therefore, he went and attempted to 'swell' their ranks with his own creations. He created a near mirror image of the pre-existing Troll's body, and went and embodied them with spirits from his other creatures (more than likely the boldogs). This would create the second 'wave' of Trolls, which would subsequently be nearly exactly like their brethren, but still from a different origin. Granted, this is nearly all speculation, but that is really all which we can work with right now.

The prospect of Trolls being dwarves stolen from Aulë is, I find, extremely unlikely. First, as Voralphion stated, how would one account for the massive size difference between the two creatures. Second, why would Melkor steal that which he could easily create? It would be well within the bounds of Melkor's powers to create a simple outer stone body with which he could animate. Therefore, why would he steal them, and risk getting caught? It is very illogical.

Voralphion -- That is a very interesting thought (outer form being animated by the will of Melkor), but how would you fit that into the plethora of different quotes, which specifically place the 'animation spirit' on orcs and the like ('like orcs -- in character and origin (Morgoth's Ring), and 'stone inhabited by goblin-spirit' (The Treason of Isengard). Although a very interesting idea, it is, I find, less likely than them being inhabited by orcs and the like, for your idea lacks the necessary textual support.

Another issue which has been raised is what creature primitive race of Trolls, assuming for the time being that my original hypothesis is true, were derived from. Were they, as Mans proposed, like Ungoliant, unknown horrors which were born into the world unbeknownst to the Vala, which had weaker, less effective orffspring (the Trolls)? Could they have been creations of one of the Valar, 'dull and lumpish', which could have been found by Melkor, tinkered with, and became the first Trolls. Or, are they neither, and are we missing some very obvious solution? An answer to this has eluded me for the time being. It will require more thought and reading on my part, and if I find and answer, I will surely post it here.