Does the number of sitemaps on Webmaster Tools affect the Google ranking at all? My website contains two different feeds of constant weekly updates and was wondering whether I should consider submitting a sitemap every week.
Sitemaps have almost no effect on rankings. You don't need a sitemap to have your pages rank well. In fact, it has been suggested that using sitemaps is a red herring. You instead should be spending time making sure your site links to all your content. See The Sitemap Paradox.
The only time that I can imagine that submitting fresh sitemaps regularly would help would be for news sites. For news articles, freshness is key to rankings. Google recognizes that for news related queries users want the latest results. These queries deserve freshness. In that case, keeping your sitemap up to date with changes could allow Googlebot to see your fresh content more readily and your site to rank better for news queries that need fresh content.