Although i recall H1 as highly valued many years ago , is there any distinct evidence to suggest that H1 is more valued than H2 tags, on a W3C compliant HTML page for the purposes of ranking in today's SERP's ?
I'd say it was all relative - Google would rate them in importance relative to each other within the page, and ignore excessive usage of any.
The heading tags are supposed to define a document heirarchy. Use the W3 HTML validation tool to generate a bullet point list of your headings. If that list does not look like a summary of your document then you are abusing the heading tags.
Is there evidence to suggest - for the same content - that a page using h1, h2, h3 does better than one using h2, h4, h6? I'd like to think there is a small benefit, but I would guess that Google understands that most sites would not use these elements exactly as they are meant to be used.