There may be ways or events in the game that trigger followers to level up, but I am no expert on it. I've also read there are level caps on them.
It too seemed to me that Meeko levelled up when he was forceably by the game (or purposely by me ) removed from the party and then rejoined on his own (or by me travelling back to the shack). But it too may have been my imagination...
I certainly have seen followers become less effective over time as the enemies levelled up! I started with Faendal at level 2 and kept him around all the way to level 54. Fairly quickly his effectiveness lagged badly. Mostly only good as a VERY temporary diversion late in the game. Remained effective against skeevers and mud crabs though.
