From the beginning, Google marked terms found as bold, italics, sentence case text, relative font size, and so forth as fancy in the index and felt this was important. At no point was it ever clear that Google assigned more weight to these fancy text terms, however, it was was matched in search more readily as a result. Spammers began to try and take advantage of the situation thinking that there was an SEO advantage. There was not. As a result, while Google may still mark these fancy terms, matches against them specifically no longer occurs- or at least not in an obvious way.
Therefore, using fancy text is not an advantage.
Related to that, while we know that the h1 tag has special meaning and indeed all headers do, I have found that they are rarely if ever matched in search. There may be some weighting of these elements terms, however, there is no clear advantage. Search matches go against semantic analysis of title tags, links, and content. Header tags are still important of course. But only in as much as semantic analysis goes. I see no evidence that header tags have weight otherwise.
Other answers that may help fill in the gaps (ignore the titles):
Can writing a floating navbar's HTML at the bottom of the page increase SEO?
Keyword phrases and links
Why would a website with keyword stuffing rank higher than one without in google search results?
Images as hyperlinks and SEO implications
What is a toxic link?
That should be enough for now.