Tiny is a Tyrannosaurus Rex that was brought under the control of the Mini-Doris that was remotely controlled by Bowler Hat Guy, who got the idea when seeing the Mini-Doris hovering over a dinosaur topiary on the grounds of Anderson Observatory. Wanting to keep it a surprise, he didn't inform Doris, who was planning on cutting the chandelier to get rid of Wilbur, and was enraged by the blatantly obvious attack as opposed to her subtle actions. After a fight with the family and Bowler Hat Guy again being told by a controlled minion that his plans weren't thought through, the Tyrannosaurus is freed from Mini-Doris' control when Wilbur shoots it off his head with Gaston's Meatball Canon and turns out to be a rather docile specimen and is shown to be acting like a puppy. Even after Doris' actions are undone by the climax of the film and he should have been sent back as a result, Tiny still appears to see Lewis back off to the past, now a pet of the Robinson household.
Tiny is essentially the opposite of Frankie. While Frankie is an amphibian given sentience and sapience, Tiny is a time-displaced extinct reptile who has a dog-like mental state. While under Bowler Hat Guy's control, Frankie's weakness is his frail body in comparison to the humans and Tiny's weakness is his huge, clumsy body.
"I have a big head, and little arms..."
"...I'm just not sure how well this plan was thought through."