A lot of webmasters leave out certain header tags because of their size e.g. they prefer to use H2 instead of H1. Its much better for SEO purposes to use a hierarchy (as already suggested by dfiocch). Use the tags in the correct order on a document, and if you want to adjust their sizes, you should do that in the CSS file.
Personally, I don't adjust the size of header tags. If search engines places bigger emphasis on larger text, then a smaller H1 tag probably won't be as effective
Yeah, you need to use H1 tags and H2 tags for SEO purposes and users. You need to style them with CSS. you do not want H1 tags as big as 50px as this would be huge and very off putting. H1 tags are just to make text bigger and draw your eyes to a certain part of a page.
As stated by dfiocch hierarchy with H tags is very important.
I did want to add as it maybe useful to some.
h1 should be used to emphasise the overall content of your page (use once per page).
h2 break down of the main topic.
h3 use as sub topic heading(s).
I've noticed a few people use multiple h2 tags. I've always held the belief each page should only have a single h1 and h2 tag. If you need to have sub topic heading you can use multiple h3 tags.
I've never experienced any dramas with ranking and have always used the above layout for h tags.
The thing about on-page content and optimization is this: you are creating a 'document' that makes sense to search engines in a fairly old fashioned, academic, scholarly way.
This means that you need to mark up the relevant content in a logical, progressive way. In, in fact, the same way as you would if you were writing a university paper.
So, you need to use the meta title tag to give an overview of what the important content of the page is about.
Then, you need to use the h1 tag to describe the main focus of the content. Further important sub-sections of your document should be titled with h2, h3 tags. Subsequent to that, bullet points and making certain phrases and sentences in bold text will indicate to the search engines what the essence of the page is about.
For me, on-page optimization is about mirroring a university paper as much as possible.
This is why citations and links to other sites within your content will also help.
You've got to keep in mind that the very clever people working at Google/Bing etc come from this type of academic background so creating a page that delivers those kind of signals is all important.