Now I'm no expert here but I read in Brophy's book on Marlin that they started putting oversize forearms on the model 1936 when it came out in 1936. They advertised them as having "sure-grip semi-beavertail forearms". Marlin was trying to update and breath a little more life into the old model 93 during the depression, trying to give them a new look along with some changes that were actually cheaper and easier to manufacture.
I agree with you I like the look of the slimmer ones best. Just started shooting a 1948 vintage 336 with the fat forearm and for function I surprisingly really like it. I think it also helps make the rifle feel a little more muzzle heavy which I like.
If I've left something out everybody feel free to set us all straight!
I can't help with the timeline but I have both. My 20" guns in 30-30 and 35 Rem. have the thin, carbine style. My long barrels, 336A Deluxe 30-30 and .444 Marlin, have the oversized forearms. All four have pistol grips. Truthfully, I never think of the difference when I pick up one or the other.