When it comes to sizing their videos on a web page, many if not most honest people will err on the side of modesty. Their biggest mistake is to make their visuals too small and timid.
Then there are those who go big, no matter what. They go big on the smallest things, and they seem to know no restraint regardless of the subject. You know the kind... don't you? They will auto-start the media and play it at full volume as soon as the page loads. They will boast the (literally) incredible features of their products or ideas using flashy and borderline tacky, explosive graphics.
Marketing is a question of balance. Tune your video to the context: turn it up and tone it down so that it is just right for the reader. Too small and you will lose your visitor quickly. Too big and you will likely annoy them to the point of no return.
Just how big is too big? The answer is: I don't know.
I don't know, because it depends on the context. It depends on the product, service or person you're promoting, the market fit and the audience you are reaching or targeting. You can read about the 5 Steps to Effective Video Landing Pages to get an idea of what to address. One thing is for sure: don't be modest. But don't blow it either* .
* If you don't know Theranos' story, you can watch serial videos recounting the full story of the startup that blew it here (abcNews.)