Answer:
Face with a tree, skin like the sea. A great beast I am. Yet vermin frightens me.
If a man would carry my burden he would break his back I am not rich But leave silver in my track
Those with eyes bigger than their stomach will definitely leave the restaurant with one of them. It is named after a house pet as well.
Tall when seated, short when standing.
Black and scary, small and hairy. In the night you hear it preach, Through its noisy high pitched screech.
I run through hills. I veer around mountains. I leap over rivers. And crawl through the forests. Step out your door to find me.