Okay, I just thought this was hilarious for some reason. My character was back home in Windhelm and needed to do some shopping, so I took Meeko along with me. Went to the Palace to pay my respects to the Jarl and told Meeko to wait because I needed to pay a call on Wuunferth.
Now you know how when you approach some NPCs, Jarls on their thrones for instance, once you get close enough they will turn and look at you and just wait for you to engage them. Well, after I walked away from Meeko I happened to look back and realized that once I got far enough away, Ulfric stopped looking at me and was looking at Meeko instead. And he just kept watching him. From a distance it was like they were having this cute little moment. Or else Ulfric was trying to figure out why I'd left this mutt for him to babysit while I went about my business.
I thought Meeko should spend some more quality time with his future daddy, so I just let them carry on while mommy had a late breakfast.
I think maybe Meeko is petitioning the Jarl for a city-wide ban on the sale of dogmeat. Also:
"How many times do I have to tell you, Borguk... Orcs won't fit through the cat door. Just use the bucket like everybody else!"