WASHINGTON ( CNN ) -- An Ohio death row inmate who says he is too overweight to be executed took his plea to the Supreme Court on Friday . Richard Cooey , 41 , and an accomplice were convicted of the 1986 murders of two college students . Richard Cooey is scheduled to die by lethal injection Tuesday and has exhausted most of his state and federal appeals . Gov . Ted Strickland earlier Friday denied the 41-year-old prisoner 's clemency petition . Cooey murdered two college students in 1986 . The justices were expected to decide whether he should receive a stay of execution , and whether to address the larger constitutional claims over when a convicted person is medically unfit for capital punishment . His lawyers have argued that the inmate -- at 5-foot-7 and 267 pounds -- is `` morbidly obese , '' and has gained about 70 pounds since his incarceration at age 19 . Prison food and confinement in his cell for 23 hours a day , limiting his opportunities for exercise , contributed to his weight problem , his legal team said in recent court filings . Cooey also says regular medication he takes for migraines will weaken the effectiveness of an anesthetic used in the a three-drug cocktail administered during execution . He says his veins are weakened because of his health issues , and the lethal drugs would amount to cruel and unusual punishment . In 2003 , one day before Cooey was scheduled to die , a judge stopped his execution on issues unrelated to his health claims . A federal appeals court ruled Thursday that Cooey waited too long to raise the medical issues , saying he `` knew of and could have filed suit over vein access prior to July 2005 . '' Cooey and a then-17-year-old accomplice were convicted of the brutal murders of Wendy Offredo and Dawn McCreery , students at the University of Akron . The men had been tossing concrete slabs onto Interstate 77 , and one of them struck Offredo 's car . Pretending to rescue the women , Cooey and Clinton Dickens took them to a remote field , according to prosecutors . There , the students were subjected to 3½ hours of rape , torture , stabbings and fatal bludgeonings . Cooey had carved an `` X '' into the stomachs of both women , prosecutors said . Each man blamed the other for delivering the fatal blows , but both were convicted of murder . Dickens received a life sentence because of his age . Cooey tried to escape from death row in 2005 , when corrections officials said he constructed a ladder from magazines and bedsheets in an effort to scale the barrier around an outdoor recreation area . At an August clemency hearing , Jon Offredo , brother of one of the victims , said , `` Our family has never gotten an apology from Richard Cooey . We 've gotten blatant lies and excuses . Is an apology too much to ask ? How could he commit such a heinous act and not feel regret ? '' But Cooey 's lawyer , Dana Cole , said his client is sorry for his crimes . The high court has not offered clear guidelines on what medical standards need to be met before an inmate is eligible for death . But in a case five years ago , the justices allowed inmates to at least make a claim that their specific physical or medical issues could be cause to block an execution . The high court had sided with a convicted Alabama killer who claimed his veins were so damaged from years of drug abuse that executioners might have to cut deeply into his flesh to administer the deadly drugs . Writing for the unanimous court , then-Justice Sandra Day O'Connor said the court was not going to `` open the floodgates to all manner of method-of-execution challenges , '' as Alabama feared . `` Our holding is extremely limited . '' That inmate is still on death row . Richard Dieter of the Death Penalty Information Center , a data-resource group that opposes capital punishment , said the Supreme Court indicated that `` how you 're going to be executed is a civil rights matter , the same as if you were discriminated [ against ] on the basis of race or gender or something like that . '' A Washington state killer was given a reprieve in 1994 after claiming he was too obese to hang . Mitchell Rupe at one time was more than 425 pounds , but weight-loss surgery in prison had reduced that to 275 pounds over the years . Subsequent legal efforts to execute him failed . He died in prison two years ago from a long illness . The Ohio case is Cooey v. Strickland .
Richard Cooey , set to die Tuesday , has exhausted most state , federal appeals . Justices are expected to decide whether he should receive stay of execution . Comment: Cooey : Drug interaction , weakened veins would make punishment cruel , unusual .