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Weinberg is a brilliant physicist and his thoughts are worth listening to. (And in this matter they are quite common among physicists.) I feel Everett (many-worlds) is by far the most sensible take on QM, though it certainly has its open questions. Weinberg's objections to it are (1) he'd prefer only one world, and (2) he doesn't see how probabilities come out of a deterministic theory. (1) is not a very good objection. (2) is a very real worry, but there are certainly ways of seemingly deriving the correct probability rule. E.g. decision theory: or self-locating uncertainty:
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Jan 5, 2017