There were no immediate reports of difficulties finding suitable veins to deliver the deadly chemicals, a problem that has delayed previous executions in the state.
Cooey's attorneys had argued that his weight problem would make it difficult for prison staff to access a vein. A prisons spokeswoman said Cooey received a pre-execution exam early Tuesday and was cleared.
Cooey, who killed two University of Akron students in 1986, walked into the death chamber at 10:15 a.m. wearing gray pants and was strapped onto the gurney.
"You (expletive) haven't paid any attention to anything I've said in the last 22 1/2 years, why would anyone pay any attention to anything I've had to say now," Cooey said looking at the ceiling. He made no other comment.
Cooey tapped the fingers of his left hand several times before he died and his face took on a purple shade.
Six family members of one of his victims watched the execution.
Summit County Prosecutor Sherri Bevan Walsh said the family was disappointed that Cooey was vulgar and hateful at the end.
He was the first inmate executed in Ohio in more than a year, and the state's first since the end of the unofficial moratorium on executions that began last year while the U.S. Supreme Court reviewed Kentucky's lethal injection procedure.
Cooey lost a final appeal earlier Tuesday when the U.S. Supreme Court turned down without comment his complaint that the state's protocol for lethal injection could cause an agonizing and painful death. He wanted the state to use a single drug rather than a three-drug combination, and asked for a stay of execution pending a hearing on that motion.
The court on Monday denied a separate appeal based on Cooey's claim that his obesity was a bar to humane lethal injection. The argument also had been rejected by a federal appeals court in Cincinnati and the Ohio Supreme Court, with both courts ruling that he missed a deadline for filing appeals.
Cooey is 75 pounds heavier than when he went to death row - the result of prison food and 23-hour-a-day confinement, his lawyers said.
They also argued that a migraine medicine prescribed by a prison physician could reduce the effect of the anesthetic used as part of the three-drug lethal injection.
They claimed that Ohio has a history of botched executions.
The last Ohio inmate to be executed was Christopher Newton - who was similar in size to Cooey - in May 2007. The execution team had trouble putting IVs in his arm, which delayed his execution nearly two hours. There were similar problems in the execution of another inmate in 2006.
Cooey made an earlier trip to the death house. But a U.S.
District Court judge intervened hours before his scheduled execution in July 2003 when the Ohio Public Defender's office said it needed more time to assess the case after an appeals court dismissed his previous attorneys for inadequate representation.
Cooey and a co-defendant were convicted in the sexual assaults and slayings of University of Akron students Dawn McCreery, 20, and Wendy Offredo, 21, in September 1986. His co-defendant was 17 and was sentenced to life in prison because of his age.
The state has now executed 27 inmates since 1999, when Ohio renewed executions after more than three decades.
