How much stack overflow earn through this great site where we can solve our problems without anything?
I don't believe how much they are making on any particular site is public information, but I do know they make the vast majority of their revenue through advertising and their jobs portal.
They don't have advertising turned on on all sites. They don't do advertising on beta sites at all and some graduated sites also don't have ads. My best guess (I don't have access to any info you don't) is that they don't bother with ads on sites that they don't have sufficient advertising partners that would be of interest to the site's target audience.
From everything I've ever seen from Stack Exchange employees, the goal really is to make Stack Exchange the best possible resource first and then figure out how to keep the wheels turning a close but distinct second. You can't keep the lights on without making sure you have revenue, but they clearly value the public good that the site does as top priority.
Advertising revenue for most of the technical advertisers on SO and the like wouldn't be applicable to the Photographer market and there isn't enough scale of page views to make sense to try to attract the right kind of advertisers for the photo site specifically. Conversely, that also means we are far less expensive to keep operating than a much more massive site like SO.
As sites grow, the cost of running them grows and so does the potential advertising value. When it gets to a point where the costs are high enough that advertising needs to help support it, the site has enough traffic to attract advertisers.