Hi There
It's questionable how much weight H tags carry at all. If they carry any, it's probably really small, or relative to how easy the keyword and industry is. H1's may help a bit more than all others - but when you start getting into H2's vs H4's it's splitting really thin hairs.
This is the best resource on H tags and SEO I know of: http://www.seobythesea.com/2012/01/heading-elements-and-the-folly-of-seo-expert-ranking-lists/