Why do I get a headache after I jog?

Yes, I'm a bit overweight, so I run outside in the morning when it's not yet so hot. I feel fine while I'm jogging: it takes me about 30 to run a little less than two miles, so I don't think I'm going very fast. When I finish, my head pounds shortly before turning into a splitting headache and I feel groggy for the rest of the day. Does anyone have any advice?