Tarkin's comment is not so much directed at Obi-Wan's age, but rather that if the Empire has continued and that this rebellion has been in existence, it would make sense for one of the last known surviving Jedi to have atleast been involved or come out and attacked. It's been almost 20 years. Do you think that if the US did not hear or see OBL for 20 years, they would still think he was alive? No, of course not. However, Vader respects the Force and respects ObiWan's dedication to it...and the theme that Lucas stresses in Prequels: Patience. Vader continuely lacks patience, even when searching for Luke and it is what brings him misfortune.
I believe the next line goes something like, "You are all that remains of that ancient religion". I think this also refers to the Empire's search and destruction of all remaining Jedi. The Jedi have become unimportant, not a worry for the Empire..and Tarkin with his massive hubris is far from concerned for Obi Wan.
As far as Obi Wan aging that much in 20 years, it might be a stretch for some...however, Obi Wan is living in the middle of a sahara style planet, in an adobe hut with very little protection from sandstorms, constant heat and sun. Look at US Presidents. Look at the amount of aging they go through in an 8 year span.