After reading this post I was stunned. Now I think the central conclusion is wrong, though I still think it is a great post, and I will go back to being stunned if you convince me the conclusion is correct.

You've shown how to identify the correct graph structure from the data. But you've erred in assuming that the directed edges of the graph imply causality.

Imagine you did the same analysis, except instead of using O="overweight" you use W="wears size 44 or higher pants". The data would look almost the same. So you would reach an analogous conclusion: that wearing large pants causes one not to exercise. This seems obviously false unless your notion of causality is very different from mine.

In general, I think the following principle holds: inferring causality requires an intervention; it cannot be discovered from observational data alone. A researcher who hypothesized that W causes not-E could round up a bunch of people, have half of them wear big pants, observe the effect of this intervention on exercise rates, and then conclude that there is no causal effect.