I posted last week about page structure and headers and their relation to SEO, today I would like to clarify something. The point i want to clarify that search engines will not care if you use h1, h2, and h3, they try to extract the featured elements in your page. That is, if you use h1, h2, and h3 and you modify the default styles to have the same font size for all headers and normal text, search engine will not assume that the data inside these headers is featured. You should give your page main header a bigger font than any other text on your page, otherwise, it is not featured on the page, and you are less likely to rank for the keywords in that header. Wait a minute, using a big font size, does not mean you will rank for it, it is one of the many things that you need to do, which i will write about it later.
Thus, your page main header (h1) which is usually close to the body tag should be relatively bigger than h2, h2 font size relatively bigger than h3 and h3 font size relatively bigger than your normal text font size.
If you feel that you need to have more than one h1 header, I would recommend you to have new pages, one for each h1 header.
Your HTML document should have a proper structure. A proper structure is defined by W3C here. All what you need to do regarding your page structure is to choose a proper page header and place it on your page as h1 element. Then develop a hierarchy for your page content and you may consider using h2, h3, etc. for each paragraph. That will make it easier for your readers to find what they are looking for, they need to look at the headers or sub headers, and read the paragraph beneath it. Search engines just like your readers will also find the page easier to understand and categorize.
I recommend you to place each paragraph with its header (h2 or h3) in html div, give the div an id, and then place few links in the top of the page that points to each sub header in your page. That will make it much more easier for your readers to navigate within your pages, and search engines will appreciate it.
It may sounds so silly to mention such things. From my experience by looking and evaluating web sites, i strongly believe that 80% or more of the web sites I looked at do a very bad job in structuring their pages.
As you noticed, I believe that the better you make the page for users, the more chance you have to rank. No one told me that, but I am quite sure that is true.