As long as the code produced is readable in a web browser then it being bloated shouldn't have much of an impact in terms of SEO. The code bloats only downside is that it might slow the page load which will have impact on SEO. Remember crawlers like Google bot essentially look at the page content in terms of textual content, what labels (alt tags etc), images and links are on there not how neatly it is presented or whether it is valid markup or not. I would take a look at your page speed otherwise I would worry as long as it is able to fulfil all the basic on page requirements such as headers, page titles etc.
Just to reiterate this - I have worked with CMS driven sites that aren't W3C compliant and don't produce the nicest html, but have loaded fast and ranked in the top 3 for competitive terms.