I was just looking at the internal evidence, pursuant to the same discussion on the WotC boards. When he arrives in Minas Tirith, Pippin gives his own height to a young man as "four feet, and not likely to grow much more, save sideways."
When Sam and Frodo return, Sam repeatedly checks Merry and Pippin's heights against his and Frodo's, and says "Can't understand it at your age, but you're both three inches taller than you ought to be." Coupled with Pippin's comment, we can infer he was three foot nine when they left the Shire.
Based on the prologue, "Concerning Hobbits," Bandobras Took (Bullroarer) was four foot five, and unsurpassed among Hobbits, "save by two famous individuals, whose queer story is told in this book." Obviously, this means Merry and Pippin. Hence, by the time the story ends (and after a few more swigs of ent-draught), we can assume that they're both taller than four foot five.