I’ve found that any heading text below the H1 tag has extremely minimal effect on SEO. I agree that it’s correct to use progressively smaller headings as you go deeper into your article, but I can almost guarantee it’s not going to do much to affect your page rank.
Google’s SEO algorithms are so convoluted, contradictory and screwed up at this point, there’s virtually no way you can build a page correctly. I have a client in my own town who has four other businesses who directly compete against him. I have done everything possible to make his website follow Google’s rules. It’s responsive. It has all original content. It has a proper page title, that is the correct length, with correct keyword usage. It has only one h1 tag, and correctly implemented h2, h3 and h4 tags. Every image has an alt tag. It has a 30% text to HTML ratio.
And yet, it is still 2nd in the SERP, and outranked by a website that is not responsive, has no H1 tag, is missing alt tags, has a 7.3% text to HTML ratio, and scores in the low 20’s on Google’s Page Speed Insights (vs my client’s site which scores in the low 50’s.)
So basically, everything that Google says will penalize a website’s rank, they are ignoring on this competitor’s site.
What’s even more nuts is that one of the things that Page Speed Insights complains about being a big slowdown on my client’s page is the Google Re-CAPTCHA code! Google creates an inefficient spam filtering tool that they encourage you to use, and then they penalize you in their SERPs when you use it!