The actor posted a video Friday just hours after news broke that his 'Rocky' costar had passed away the day prior -- and you can tell Sly is absolutely torn up about it ... fighting back tears as he honors his longtime friend and companion in the ring.

Sly says he owes so much of his career and success to Carl ... noting the man had a magnetism and energy about him that made him so special -- especially for the 'Rocky' franchise. SS recounts first meeting Carl ... and knowing right away, this guy's a star.

This video was actually filmed with Sly standing in front of the famous painting that was commissioned to recreate the end of 'Rocky III,' where they face off in the ring anew.

Sylvester ends his gut-wrenching remarks here with a special message for his good friend -- "Apollo, keep punching."

He also adds this of the late Weathers ... "We lost a legend yesterday. My life was forever changed for the better the day I met Carl Weathers. Rest in power."

We couldn't have said it better ourselves.