Kasparov was lauded for his dedication to fitness during his title years because he took "long walks." If that doesn't tell you all you need to know about the level of fitness inherent in this pastime, nothing will.
Chess players, on the whole, are marshmallows. You don't get fit sitting at a table or reading a book. We may be fitter than poker players, however.
Research groups:
By Level
1100-1500
1500-2000
2000-2400
2400-2600
2600+
By Age
8-20
20-30
30-40
40-50
50+
It would be interesting to know the relative obesity rates...
What do you say?