Here is the difference between descriptive and prescriptive grammar, also the difference between English majors and Linguistics majors, both categories into which I belong. One tells you what to do--prescriptive grammar as explained by English majors--and the other tells you what is actually going on--descriptive grammar as explained by Linguistics Majors.
So here it is:
"You better not..."
"You better be..."
Have you noticed this? Have you been "corrected" by an English major?
Well, of course the modal-like word better is "missing" from the sentences:
"You had better not ..."
"You had better not ..." became "You'd better not," which is perfectly fine.
But then this contraction reduced the saliency of the voiced /d/, which transitions into the next voiced consonant, /b/, in the second part of the modal-like you'd better, helping that /d/ disappear by having it's voicing still there, sort of. Because this voicing is still there in the /b/, the voicing in the /d/ became redundant, sort of. Native speakers can figure out the meaning without both voicings, so why have them? Grammatical minimalism kicks in here.
Of course dropping the had has become perfectly acceptable in daily conversations between native speakers. This is a grammatical change that is happening right before our eyes. In some time,
You better be careful
Will be just as correct as today's:
You had better be careful.
And you know what that means? Some grammarian eventually will look down on you for not using it correctly.