This is metro-area-level information, so we can't explain away the drop in 35-44 with "people moved to the suburbs." What does probably explain it is high total emigration among that age cohort. The population of that age group in Greater Cleveland has dropped 18% over the seven-year period for which data is available. Every other age group grew.
Wow, that difference is stark. It bucks the conventional wisdom that we're having a hard time holding on to young people. Who are the people who are leaving? Let's examine the percent changes of the specific age cohort 35-44 over the same time period.
The data doesn't reveal any solid trends -- there was a mass exodus of college-educated people in 2008, but not in other years. It appears that more non-college educated left post-2009, causing the percent of degree-holders to rise. If I had to guess at this one, I'd say that most of these 35-44 year-olds hold middle management jobs, and are either the victims of downsizing or corporate consolidations demanding that they move to another employment center in order to keep their jobs. Since this age group is most likely to have young children, they're more concerned about paying the bills than the other age groups, and are probably going to be more willing to acquiesce to an employer's demand to relocate rather than try to tough it out in the open job market.
Food for thought. If we figured out a way to increase retention of this specific age group, we could see the metro population head upward again. We're not far.