In the mainstream comics, Messiah War Part 2 (Cable #13), we see the 800 year old and 1000 year old Deadpool. His typical super-cancer face and skin. Since he doesn't have the typical old man hair or wrinkly skin clues that we expect from someone having aged, all we have is his statement that "I'm not healing like I used to." We also know that Wolverine ages slowly due to his mutant healing factor, and since Deadpool has a copied version of that, we know that Deadpool must age.
800 Year old:
1000 Year old:
He doesn't look any different 200 years later. His eyes are redder, but that's likely just a X-Force related stylistic choice. Wolverine here has time-jumped, while Deadpool took the long way round.
In regards to the movie:
Wade is no longer just given a copy of Wolverine's mutant healing ability. Instead, he is forced to develop his own. The depicted scenes in Deadpool and X-Men show that Wade and Logan have similar healing times for minor wounds. Wade is shown to take days to regrow his hand, which is taken from his first ongoing comic series, where his healing factor is significantly reduced to the modern levels. The constant comparisons to Wolverine would seem to indicate that the production intends for Wolverine and Deadpool to have similar levels of healing as they would in the comics. We have seen that Wolverine has only aged a bit since his colonial era date of birth ("He could be older than you, Professor" line in X1). Ergo Deadpool will likely age at the same rate. But we have yet to have a full answer in Movie canon.