According to formal grammatical rules, this construction is subjunctive. So, technically, the correct wording would be this:
"It is high time that you stop smoking."
However, in everyday English usage, the past form of the verb is often used:
"It's high time you stopped smoking."
Likewise, "you better" is not formal English. Even in colloquial English, the phrase is correctly "you had better" or "you'd better"; so "you better" is actually incorrect, but it is commonly used and understood.
"It's high time" and "you better" mean approximately the same thing, and so the use of both would be redundant. That is, you should choose one or the other:
"It's high time you stopped smoking."
"You better stop smoking."
Again, neither is grammatically correct, but they are acceptable in colloquial speech.
"High time" is something that makes the speaker sound lofty and condescending. One can imagine a raised nose and sharp tone from the person saying it.