At a hotel breakfast table, Caspar Weinberger, who recently resigned as secretary of defense, is cheerfully rattling on, and some of his listeners are rolling their eyes upward in an unmistakable ''oh, brother'' expression.

It is something you see often when Weinberger and his boss, the president, are meeting with newspeople to explain and defend their policies.

The big eye-roller is Weinberger's claim that the record defense budgets he's administered for seven years have had nothing -- nothing! -- to do with the recent string of Reagan era mega-deficits. The budget is out of balance because Congress refuses to cut ''domestic spending.'' As usual, Weinberger speaks so amiably, so unaggressively, that listeners are more entertained than appalled by the whoppers, like adults listening to the tall tales of a precocious and imaginative child.

The question, still unanswered as he leaves office, is whether this master of the military-industrial tall tale is bluffing or not. No one knows. That is the Weinberger enigma.

He will say something like, ''We've asked the Congress for a small mobile missile.'' But everyone is aware that his own procurement officials at the Pentagon have waged unstinting war against the Midgetman. It's been all over the papers.

Not everything Weinberger says is implausible. Like the president, he is better at generalizations than facts. The Russians, he boasts, have now eaten every threat they made to boycott arms-control talks. That they're about to sign the intermediate-range nuclear force treaty on Reagan's ''zero-option'' terms is a tribute to the administration's steadfastness. He has a point.

Otherwise, however, in defending the treaty he is soon deeply enmeshed in contradictions.

It is true, he admits, that he has complained much about the imbalance of conventional forces in Europe, which many Europeans (and the recently retired commander of NATO, Gen. Bernard Rogers) fear will be aggravated by the INF treaty. He supports it all the same.

Yes, the Russians have cheated on the anti-ballistic missile treaty. But no, that fact, if a fact, shouldn't disquiet the Senate or the public about INF. Verification's never perfect.

Again on the subject of spending, someone asks the former secretary whether all the U.S. borrowing of recent years might not someday restrain our freedom of action. Not at all, Weinberger says. Much of California, his home state, was developed by British and French and German capital. It's nothing new.

But might the precarious indebtedness expose the United States to the sort of jam the British got into in 1956, when a run on sterling forced them to scrap the Suez operation?

Nothing of the sort, Weinberger insists. ''They withdrew -- and they didn't really have to -- because the Labor politicians wanted to go on winning elections.''

But, sir, someone says, the Conservatives, not Labor, were running things -- Sir Anthony Eden himself. And everyone remembers the dangerous run on sterling. No, Weinberger insists. It was all Labor's doing.

Weinberger, as before, favors a ''first-phase'' deployment of a missile defense in the early 1990s. When asked to say specifically what technology he has in mind, he cites an anti-missile system that's been around for years, now dressed up in new jargon (''kinetic-kill vehicles''). He speaks of its being stationed ''out there,'' but if ''out there'' means space he is wrong. It is an old-fashioned atmospheric system.

Eyes roll.

One theory is that the real Caspar Weinberger isn't at all the fantasist he sometimes sounds like and fudges facts he is perfectly well aware of because he believes his ultimate goals are sound. Also, he knows the public pays little close attention to esoteric arms and strategy issues.

Others, and they are a number among Washington students of strategic matters, view Weinberger as a bright bookkeeper well over his head in a game beyond his ken, taken to the cleaners by more assiduous students of detail with stronger ideas. In this theory, Weinberger is to strategic matters as Reagan is to fiscal policy.

Certainly Weinberger, like his boss, lives in an undemanding intellectual climate where imagination seems a larger component than history or analysis. But the call is hard to make for sure. That is why Weinberger is no less an enigma today than when he went to preside over ''the rearming of America'' seven years ago.