Looking for romance drama where either one of the leads behaves in a pet-like or cute way or is treated like a pet by the other lead. For example like the girl lead in Heart to Heart or like in the movie A Werewolf Boy.

Kimi wa Petto (you're my pet)
The female lead in Oh My Ghost, who is played bu Park Bo Young, (the same actress as A Werewolf Boy!) is very short and cute. The male lead is always patting her on the head, or referring to her tiny size -- so while he doesn't treat her as a "pet", he does treat like this sweet and small thing.

Edit: oh and I forgot My Girlfriend is a Gumiho! The female lead is a nine tailed fox, and has certain animal habits, like eating ridiculously huge amounts of meat and such. She's also one of the cutest characters in dramaland ever, as she's bright, earnest and quite innocent. However, the male lead doesn't really treat her like this cute pet -- he's rather afraid of her, which is more for the comedy though because it's so obvious the female lead is adorable.
only main leads or do second ones count? 

in You are Beautiful, the main girl is like a shy puppy with the second guy, leading to many awkward yet adorkable head-pats.. lol ;P 

in Reply 1994, "shy puppy" also accurately describes the boy who crushes on the main guy- cue not just head-pats, but chin-tickles too xD 

& almost forgot to add- both leads in Mary! they even get to point of barking/meowing at each other loool.. stray pup & kitty gurl OTP! ♡ 
Shan Shan comes to Eat
how about following the girl around with a puppy-like adorableness and determination?
Yeo Joon Hee from Heartstrings
One Pound Gospel