This is not necessarily a story I have been following closely, but it is a story that has some interesting legal implications. I have written about this particular case here.
Richard Cooey is a convicted rapist and murderer. These are charges that he has not denied. He was convicted of raping and murdering two young women in 1986. However, as he was waiting on death row in Ohio he also gained a considerable amount of weight. I guess sitting around 23 hours a day doing nothing much in one's cell could lead to a weight problem. Perhaps prisons need to work out how to give death row inmates more time for physical exercise. He weighed in at an impressive 125kgs.
Cooey had claimed that his obesity would mean that a lethal injection was tantamount to cruel and unusual punishment and as such prohibited by the provisions of the US Constitution. The other claim that Cooey's lawyers were arguing was that Cooey was taking a medication that would adversely impact on the effectiveness of the lethal injection drugs and cause him to suffer unnecessarily.
The appeal to the Supreme Court was denied by Justice Stevens. Justice Stevens is one of the more liberal justices of the current Supreme Court.
Simply, executing overweight or obese people is no less constitutional than executing death row inmates living within the "healthy" range, at least, as it relates to weight.