Or more specifically, Gandalf - as an extra-dimensional intelligence prosecuting the latest phase of a conflict literally older than creation - took an interest in the precursors of the Hobbits and began deliberately cultivating them as a sort of ‘counter’ to the threat of Sauron's growing influence in general and to the One Ring in particular. My evidence for this (admittedly rather ‘out-there’) theory is as follows:
Firstly, Hobbits and their close relatives seem to be incredibly resistant to corruption from Sauron and the Ring. Sméagol/Gollum held onto the thing for millennia and retained a large portion of his own will, to the point of unknowingly keeping the Ring away from Sauron for a very long time. Bilbo had the Ring for decades with only a few latent effects on his personality. Frodo holds onto the Ring for more than a year in a very high-stress situation before he starts to crack. Sam outright rejects it for a short time in Mordor itself. All it takes is a few weeks of mere proximity for Boromir to go off the deep end and try to take the Ring by force. Further, Frodo is able to survive the Morgul-dagger for a length of time that surprises Gandalf and Elrond both. Sam, meanwhile, manages to strike a blow against Shelob, which apparently no other creature had been able to do before. Random mutations? Or signs of an active intelligence deliberately meddling with the Halflings' genome?
Secondly, Hobbits seem to be born infiltrators. In The Hobbit, Gandalf actively markets Bilbo - who has explicitly never met him before - as a ‘Burglar.’ A while later, with precisely ZERO training, Bilbo is able to sneak his way through an Ork-held mountain while carrying a glowing sword - BEFORE he picks up the Ring. He is then able to carefully tiptoe around Smaug with a surprising degree of success. In the Trilogy proper, Frodo and Sam are able to mount a multi-month stealth mission with relatively few issues, never being detected by anything larger than a local patrol and even posing as Orcs for a short while. This matches up perfectly with what I have read of Gandalf's modus operandi, which itself seems to resemble an almost Green Beret style of training up singular champions or small teams to serve specific purposes in the conflict with Sauron. Even the Hobbits tendency to be almost docile unless cornered could be considered a bonus when examining their possibility for stealth.
Thirdly, for a spirit supposedly sent to aid the whole of Middle-Earth against Sauron, Gandalf seems to have an unusual preoccupation with the Shire and it's inhabitants, to the point of entrusting it's defense to the Rangers and repeatedly coming to spirit away particularly adventurous Hobbits who are almost never seen again. The idle indulgences of a wanderer seeking a place of rest and innocence? Or a world-shaping spirit, coming back to check on his personal pet project and get promising lineages interested in each other?
Finally, I think it would just make for some interesting irony and drama for Gandalf when looking at the Uruk-hai project of Isengard.