Weak forms of HAVE

According to Longman Pronunciation Dictionary

HAVE: The weak form /v/ is used only after a vowel (when it is often written as the contraction ’ve), or in very fast speech at the beginning of a sentence.

Weak forms of have, has, had are used when the word is the equivalent of have got and is used with an object that is not a pronoun.

What does object that is not a pronoun exactly mean, and why does it not license a weak form?

Solution 1:

An "object that is not a pronoun" is an object of the verb that is not a pronoun. It's usually a noun or a noun phrase:

I've her concert tickets here,
I've the things you wanted in the trunk of my car.

but it could be other parts of speech as well. See Wikipedia.

Why does a pronoun prevent a weak form?

Probably because pronouns are typically not stressed, and English doesn't like putting too many unstressed words in a row. So if your object is stressed:

I've three tickets to the concert,

you can leave have unstressed, and this lets you use the weak form instead of the full pronunciation. But if you use a pronoun, it's generally unstressed, and that automatically puts some stress on have:

I have her under surveillance.

(Note that the rules about stress in English are more complicated than what I've explained above, and that the stresses I've indicated aren't the only way of stressing the words in these sentences.)