Burt Young died from cardiac arrest. He had an assortment of heart issues.

If you look closely at all the Rocky movies whenever Paulie is present at ringside or participating in the ring-walks, he always gives his best/redeeming moments in those scenes:

ROCKY I-He lifts up the ring-rope (As well as distracting security) so Adrian can get in the ring to embrace Rocky.
ROCKY III-"You did good, Apollo".
ROCKY IV-"....but if I could just unzip myself and step out and be someone else, I'd wanna be you".
ROCKY V-One could say he (Momentarily) becomes the sacrificial lamb to Tommy Gunn when confronting him in the bar. Oh, and since "The ring" was outside, I'd say it counts.
ROCKY BALBOA-He asks Rocky if "The stuff in the basement" is finally gone now.

I always loved this moment...also ringside...