I don't know why it being veto proof would make a difference when it comes to signing statements. If I remember correctly Obama did a number of signing statements.

http://www.coherentbabble.com/listBHOall.htm

Meaningless? Maybe.

it carries no real legal significance. a court might pay attention to it somewhat akin to the way they sometimes pay attention to congressional intent, so it might carry some influence, but there's nothing binding about it.

it really doesn't mean anything more than whatever throwaway words a president says at the signing ceremony.

The point of them is basically putting congress on notice that he intends on interpreting it differently than they suggest. As such, it is seen as giving him "cover" for impeachment. It can also be a way of influencing any Supreme Court arguments. "Intent of Congress" is often considered in SC decisions. The thought (never tested) is that a signing statement permanently indicates the "intent" of the President when signing. They hope that influences the court and there is even some thought among some Federalist types that an SC court rule a law "invalid" because the presidents assertions in a signing statement indicate that if it had been known that those assumptions were invalid, then the president wouldn't have signed the bill.

Of course the creep will try to act like it does. There's no way he has the mental capacity to realize that the fancy legal argument he signed Ian's holy writ.

I believe they carry no legal weight except they might be used as evidence in case a president fails to carry out a law and gets taken to court.