Dog park fight

Big dog and little dog fight. Who is in the wrong/responsible for vet bills?

Both at the large dog park, park is meant for large dogs and has a 20lb minimum. There is a separate area for dogs 20lbs and under. Little dog is less than 10lbs, big dog is around 60lbs. Big dog gets over excited around little dogs, she goes up to the little dog very energetic and sniffing/licking the little dog. Little dog gets scared and goes after the big dog, biting and snarling. Big dog retaliates and bites the little dog. Little dog now has substantial injuries. Is it the big dogs/owners fault because big dog injured the little dog? Or is it the little dogs/owners fault because they were under the weight limit and the little dogs started the altercation?