I just wonder whether this sentence:
It is on you.
can ever mean this one:
It is because of you.
This was spoken Tony Stark in the 2012 film, The Avengers.
Is “It’s all on you” a common and natural saying in English-speaking countries?
It generally means "it is your responsibility." By responsibility it means that the blame or the victory would belong to you - sometimes it is said when someone is taking a risk or doing something that could go badly. The person saying it means "it is your choice, but don't blame me if it fails." Particularly in superhero movies where people are doing dangerous things all the time.
"It's all on you" could mean:
It's all because of you (you're at fault, you're the reason everything failed)
It all depends on you (you're the only person responsible for this task)
In both cases, it's a question of responsibility - either for something that has been already done (but often poorly) or that may go wrong in the future, or for something that still needs to be done (and may be a large task).
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