You'd ( had better ) better not eat so much chocolate - You should not eat so much chocolate.
The idiomatic phrase “had better” (as in “I had better study” or “We’d better go”) is a venerable usage with roots far back in Old English.
The shortened form “better” (as in “I better study” or “We better go”) dates from the 1830s and is used informally in both British and American English.
In fact, Fowler’s Modern English Usage (rev. 3rd ed.) says it’s not unheard of in your neck of the woods: “In practice this use of an unsupported better is much more common in North America, Australia, and NZ than in Britain.”
Using “better” by itself is FINE except in formal English. “In a wide range of informal circumstances (but never in formal contexts) the had or ’d can be dispensed with,” Fowler’s says.
Merriam-Webster’s Dictionary of English Usage calls “had better” a standard English idiom and agrees with Fowler’s that “better,” when used alone in this sense, “is not found in very formal surroundings.”
The OED says the abbreviated usage originated in the US, and labels it a colloquialism. But Merriam-Webster’s Collegiate Dictionary (11th ed.) lists it without reservations.
The Merriam-Webster’s editors give the example “you better hurry,” and say “better” in this sense is a “verbal auxiliary.”
It should be noted that even the full phrase, “had better,” was criticized by some in the 19th century on the ground that it was illogical and couldn’t be parsed.
As Rolfe and Hersey write in a footnote: “This is essentially the familiar grammar-monger’s objection to had better, had rather, had as lief, etc., that they ‘cannot be parsed’—which is true of many another well-established idiom, and merely shows that the ‘parsers’ have something yet to learn.”