It is important to keep your head down and raise you hips up to the surface. This allows your body to flow through the water more easily. In a longer swim you really should keep your head down like you are looking at the bottom of the pool.
If you feel like your body is sinking it is probably because you are taking a shorter stroke on the other side, you are lifting you head, or you are letting your hips sink. When I was taught how to swim I was told that it is important to bi-lateral breath as well. I think it is important to keep your body balanced in the water but I don't think it is neccesary to breath to both sides. I've been swimming for my entire life and all through college and I found that if you are stronger breathing to one side then you should just stick with doing that. If you watch all the Olympians, specifically Phelps, Lezak, and Vanderkay, you will notice that they only breath to one side during their entire race.
Just something to think about.