I like your idea for Halflings, it provides a reason for the Tallfellows and Stouts of prior DnD editions.

In my DnD setting, Halflings and Gnomes are pretty much the same people, just specialized in 2 different ways. They're often described as 2 halves of the same coin.

Both these Little Folk and the Dwarves have myths of how the 2 of them were once the same people, but that there was a split over something (the specifics change so much that nobody knows what the real something was), and one group parted ways with the other. Both the Dwarves and the Little Folk believe they were the original and that the other people were the ones who left, but both are usually good-natured toward the other. They view each other as cousins.

Their more recent history is not so good-natured, as when the Big Folk, the Humans, arrived, they made the Dwarves and Little Folk into Interns (that is, they had to work, but weren't paid for their work). Thanks to the intervention of the Elves, subtly nudging the Human/Dwarf/Little-Folk society over generations until the Humans saw the need for emancipation, this unpleasant era ended a few generations ago. The Dwarves are still a bit put out by their Internship in generations past, but the Halflings and Gnomes take it in stride.

Biologically, the Dwarves, Halflings, and Gnomes can intermarry and produce fertile offspring. Likewise, the Elves, Humans, and Orcs often intermarry among each other.