As always, blame the Kender
tl;dr Originally halflings were h*bbits (R) straight out of Tolkien, with "slightly pointy ears". D&D had to distance itself from hobbits, with "halflings" like pint-sized humans. Kenders are the first D&D halflings to have really pointy ears.
Though in the Hobbit I don't think the ears of halflings are mentioned, Tolkien did describe them as:
A round, jovial face; ears only slightly pointed and 'elvish'; hair short and curling (brown).
OD&D Hobbits become AD&D Halflings
There is very little physical description of hobbits in Chainmail (which just calls them "little chaps" or in Men and Magic (which just refers the reader to Chainmail), but as is well known at the time of OD&D, TSR got into trouble with the Tolkien Estate and had to rename the creatures "halflings".
By the time of the Monster Manual (1977), Halflings are pictured with rounded-ears, looking like small humans, and described so in the first Player's Handbook (1978)
Halflings are very much like small humans, thus their name.
This may have been a deliberate attempt to distinguish D&D "halflings" from Tolkien's "hobbits", taking the literal meaning of "halfling".
Enter the Kender
In Dragon #85 (1984) there is a short story by Roger E. Moore which first introduces the race of Kender in the person of Tasselhoff Burfoot:
The intruder was barely four feet in height and thinly built; he had bright brown eyes and the face of a ten- year-old human child. Narrow, pointed ears pressed against his light brown hair, which was pulled into a sort of ponytail on top of his head.
This distinction then became established in AD&D 2e, with 'vanilla' halflings continuing to be described as "short, generally plump people, very much like small humans. Their faces are round and broad and often quite florid." (2e PHB), whereas Kender have "distinctive pointed ears that give them an elven appearance." (Monstrous Compendium: Dragonlance)
I don't know the ins and outs after these beginning, but between the de-Tolkienised halflings and the elf-like Kender we have our two sorts of halflings, with Tolkien's original description of hobbits somewhere in between. It seems that Pathfinder chose the Kender-like appearance, though fortunately without the personality traits of those little... (Hang on, where's my purse?)