People can give "critical" a bad name (blind anti-sequel hatred, etc.), but critical thinking has so many benefits in all areas of life.
Now, I'm not suggesting that the story of Mr. Peabody & Sherman was much similar to Meet the Robinsons. And the dog with glasses was only a joke in that movie, not a main character (though I got a good laugh when my mom searched and found out there was apparently at least one decent-quality figure made of it!). And while it is definitely true that the similarities I see between these two movies are nowhere near as clear or as numerous as those between Frozen and Tangled, I do think it's more than just "young boy + time travel." It is in fact just the most recent example of an animated film prominently advocating adoption like Meet the Robinsons (and Despicable Me). Additionally, the rather dark looks Penny gives Sherman early on definitely remind me of...the kinda goth girl from Meet the Robinsons whose name escapes me but is very clearly the main character's future wife. I wouldn't want to say that I think no other movies influenced it, though, as the wide selection of crazily-interacting historical figures definitely drew from the Night at the Museum films (note prominent inclusion of ancient Egypt).
However, you opened up a really interesting perspective for me by saying Big Hero 6 seems similar to Dreamworks. Shortly before I VMed you, I told my youngest brother that I thought some Wreck-It Ralph themes might come into play, especially considering Baymax's size. But a few hours after I VMed you, I realized that the way Baymax moves and carries himself is much more reminiscent of a Dreamworks character: Po from Kung Fu Panda.
Oh, BTW, I probably should have said that I liked your "custom trainer title," as I've been thinking of changing mine to something Christmas-related as well.