The champion had led by three entering the final round.
"I reckon everyone else must have struggled a little bit today," Weekley said.
Kim had started the round in second-place and ended up with his second top-five finish of the season after carding a 71. Baddeley shot a closing 69.
Jim Furyk also posted a 69 to finish fourth at 11-under 273.
Cliff Kresge was fifth and Jason Bohn sixth.
Jeb Bush 'thinking about running for president' in 2016
Joan Rivers refuses to apologize for kidnapping joke