Initially spotted playing for London amateur side South Ruislip Rangers, Karleigh was recruited by Brentford in 2004. Joining the likes of previous academy graduates Paul Buckle, Keith Millen, Marcus Bent and Jake Reeves, Osborne quickly made an impression in the Bees' youth system after moving back from attacking and midfield roles.
By September of 2004, he was named as a substitute for a first-team cup tie, and he played all 90 minutes of three senior games the following season before a loan spell at Hayes. New Brentford manager Leroy Rosenior would back Osborne in the 2006-07 campaign, playing 24 times in a difficult season, falling to relegation from Sky Bet League One. The Griffin Park side would stabilise themselves the next season, with Osborne playing an important role, playing 31 times, captaining the side on numerous occasions and scoring his first senior goal - heading home a corner from former Pilgrim Ryan Dickson.
Surprisingly, the defender spent much of the opening part of the following season on loan at Oxford United and Eastbourne Borough, but would return to Brentford and score four goals in 26 appearances as they clinched the League Two title. The 2009-10 season for Karleigh was blighted by injuries, but good form upon his return earned him a new contract with the London club. He repaid the gratitude shown in him by playing 51 games the following season, and passed the 150-appearance mark for Brentford before turning down a new contract to join Millwall in the summer of 2012. Karleigh signed a two-year deal to join Kenny Jackett's Lions, but would struggle to get first-team opportunities at The Den.
He played 16 games in his first season there, followed by just one more in the 2013-14 campaign, which he would finish at Bristol City, playing eight times and impressing enough to earn a move to Ashton Gate. Osborne would play 20 times for the Robins, either side of a temporary spell at Colchester United. Karleigh spent a large part of last season on loan with AFC Wimbledon, making 23 appearances, but a knee injury picked up in February during training meant he would miss out on Wimbledon's late run to the play-offs and eventual promotion to League One.