What is important for me about a website is it’s content. If the content is good enough, I keep coming back as long as it is worth the visit.
This means that I will tolerate advertising (everybody understands it is the advertising that pays for a website) as long as it does not get too much in the way. More usefull websites get away with more obtrusive advertising.

For me, as sponsored posts are becoming more common, this does not have any effect on a websites credibility – as long as I understand it is an advertisement.