Since the words toward and towards—as used today in the sense of "in the direction of"—are identical and interchangeable, the choice of which one to use is strictly a style question.
The first U.S. discussion of toward versus towards that I'm aware of appears in Joseph Hull, English Grammar, by Lectures: Comprehending the Principles and Rules of Syntactical Parsing, on a New and Highly Approved System, seventh edition (1833):
Many barbarous words of uncouth sound are still used by our best speakers and writers, notwithstanding there are those of the same import more pleasing to the ear; as whilst for while; amidst for amid; downwards for downward; upwards for upward; towards for toward; amongst for among; betwixt for between.
Unfortunately for a modern reader, it isn't clear whether the italicized words are the "barbarous words of uncouth sound" or "those of the same import more pleasing to the ear." On balance I suspect that Hull considered the versions marred by an extra x or s to be of uncouth sound, but if he meant to condemn towards, he was doing so without the backing of Noah Webster's An American Dictionary of the English Language (1828) which treated toward and towards as interchangeable with regard to the senses "in the direction of," "regarding," "tending to," and "near."
Perhaps the most significant development in the U.S. rivalry between toward and towards involves the treatment of the two words in the 1847 edition of Webster's An American Dictionary of the English Language: Without any explanation, towards simply vanishes. And when it reappears in the 1864 edition of that dictionary, it does so only in the form of a one line entry reading "Towards. Same as TOWARD." Coequal treatment of the two forms doesn't resume until the arrival of the first Webster's International Dictionary (1890).
In any event, the next commenter on toward and towards, Alfred Ayres, The Verbalist (1896) is less ambiguous about his contemporaries' preferences:
Toward. Those that profess to know about such things say that etymology furnishes no pretext for the adding of s to ward in such words as backward, forward, toward, upward, onward, downward, afterward, heavenward, earthward, and the like.
U.S. reference works from the past 70 years or so are remarkably consistent in anointing toward as the preferred U.S. spelling, but not one of them analyzes the change in U.S. usage that brought this state of affairs about. From Bergen Evans & Cornelia Evans, A Dictionary of Contemporary American Usage (1957):
toward; towards. These forms are both standard English. In Great Britain the form towards is heard more often and toward is considered archaic or Biblical. In the United States toward is the preferred form.
From Theodore Bernstein, The Careful Writer (1973):
TOWARD(S) In the United States the favored form is toward; in Britain, towards. [Cross reference omitted.]
From Roy Copperud, American Usage and Style: The Consensus (1980):
toward, towards. The second form is generally considered preferable in Britain, the first in the U.S., though the second is gaining favor in this country. Both, of course, are standard.There is a notion that towards goes with tangible objects (towards a table) and toward with intangibles (toward an understanding) but this is fanciful.
From The Associated Press Stylebook and Libel Manual (1980):
toward Not towards.
From Webster's Dictionary of English Usage (1989):
toward, towards Many commentators have observed that toward is more common choice in American English, while the preference in British English is for towards. Our evidence confirms that such is indeed the case. Both words are commonly used in the U.S., but toward is undoubtedly prevalent: [examples omitted]. The British strongly favor towards: [examples omitted].
At one time some critics (as Ayres 1881) preferred toward because they believed the -s of towards had died away. Letters from our correspondents sometimes seem to be seeking some semantic basis for a differentiation between the forms, but there is none.
From Kenneth Wilson, The Columbia Guide to Standard American English (1993):
toward, towards (preps.) Toward and towards (pronounce them either TORD[Z] or TUH-WORD[Z]) are Standard and interchangeable in meaning. American English uses both, but toward more often; British English uses towards more.
Patricia O'Conner, Woe Is I (1996):
toward. No final s ("towards"), although that's how they say it in Britain. Similarly, in American English, standard practice is not to add a final s to forward, backward, upward, onward, downward, and so on. [Example omitted.]
From Allan Siegal & William Connolly, The New York Times Manual of Style and Usage (1999):
toward (not towards).
And from Bryan Garner, Garner's Modern American Usage (2003):
toward.A. And towards. In AmE, the preferred form is toward; towards is prevalent in BrE. [Cross reference omitted.]
In the book's entry for "DIRECTIONAL WORDS," Garner makes these comments:
In AmE, the preferred practice is to use the -ward form of directional words, as in toward, forward, and westward. Words ending in -ward may be either adjectives or adverbs, whereas words ending in -wards, common in BrE, may be adverbs only. [List of preferred U.S. forms omitted.]
An exception in AmE is the adverb backwards, which is used frequently (though still much less often than backward). (It's anomalous that many people who say forward also say backwards.) ...
So there you have it—decades of observing that toward is more prevalent than towards in the United States, but no explanation of why.
In my years of work as a freelance and in-house copy editor, I've noticed that U.S. publishers commonly specify the use of toward, just as AP and The New York Times do. Old-fashioned publishers like the idea that all of the books they publish follow a consistent house style—and that, of course, makes an arbitrary style preference self-perpetuating. As publishing moves away from enforcing house styles and toward a "we can't afford to worry about that kind of stuff" model, I think you'll see an increase in the frequency of towards in U.S. publications, since the preference for toward was never as strong at the manuscript stage as it was on bookstore shelves.