It seems that dolphins have (among?) the highest encephalization quotients found outside of humans, higher even than chimpanzees. By the "use it or lose it" principle this indicates that intelligence must be particularly valuable in their niche. Why is that? They are predatory and social, and both of those are associated with intelligence, but why are dolphins smarter than other predatory pack animals? For example, is there something about being an air-breathing organism living in water that makes having a high EQ particularly adaptive?
It's less about the brain size, I think, more about the metabolic cost of brains. Brains are among the most costly organs to keep what it comes to oxygen demand. Air-breathing increases available oxygen for the body, hence mammals have larger brains that for example fish.
In diving animals the metabolic cost of brains is connected to the diving time (can't find the reference at the moment). Sperm whales shut down parts of their brains on long dives and do not have particularly active brains in general. Dolphins are mostly shallow diving animals. Maybe the selection favors higher brain metabolism potentially increasing the ability to catch prey and avoid predators? Pure speculation, though.
It might not fully answer your question…
Cost of having a heavy brain
Generally speaking, having a heavy organ is an important cost for flying animals, a medium cost for terrestrial animals and a low cost for marine animals. Loosely speaking, the principle "use it or lose it" does not apply with the same strength in all animals in regards to brain weight. If you create a regression between "intelligence" and "need of being intelligent"(supposing it means something!) in terrestrial mammals and add the dolphin on your graph, you might be surprised that the dolphin does not fit on the regression but it might only be due to the fact that they live in water which is much more dense than air so that it is less costly to carry a big brain. So, yes there might have something to do with "living in the water".
Indexes of intelligence
EQ does not mean intelligence! It is just an index. And we have to understand that people first were happy to think that humans are very smart because they have a big brain but they were terribly confused when they've learned that sperm whales brain weight 8kg! So they tried finding other indexes. EQ is one of them and we're quite happy to use it because it places humans at the first position. But it does not mean that this index is a good representation of intelligence. Some small birds with their tiny brain were shown to be have a spatial memory that is much more efficient that the one of humans for example.
Something else. When looking at these indexes one should not forget that size (or weight) does not equals efficiency. Let's make an analogy with computers. You can have a good software or a good hardware. Big brains are not necessarily very efficient!
Now, it is still true that dolphins are good at performing many tasks that we link to the concept of intelligence. Dolphins have complex social organization that is probably link with their intelligence. I would tend to think (just a guess) that there are many social factors involved into the evolution of their cognitive abilities. Because the social structure changes as cognitive abilities evolves, it seems to me quite hard to know what factors made that clever individuals were more fit than stupid ones at every moment during the evolution of dolphins. But I might overlook the complexity of the problem. And I honestly never learned any article concerning the role or the evolution of cognitive abilities in dolphins.