Weight is always a concern with backpacking food you'll be carrying everything on your back. Some will tell you to find your weight savings in other areas, and argue for the necessity of healthy, meaning heavy, food. My experience, however, tells me that we can enjoy lighter loads and worry less about healthy food on short trips.
In the Sierra Nevada I ate more than 60 granola bars in five days with no ill effects. No stove meant a lighter pack, and it was very convenient to not cook. Of course, I usually supplement my backpacking diet with berries and other wild foods, so it probably wasn't all that unhealthy.
Different Foods For Different Backpackers
Each of us is unique. I don't suffer when I have no cooked meals, but you may. There isn't a one-size-fits-all solution to the backpacking food question. You have to balance the weight/health/taste/cost issues in your own way. Consider the following points, though, in making your choices.
The lightest food is that which has the most calories per ounce. Pure fat wins the contest (oils), followed by high-fat foods (nuts), low moisture carbohydrates (granola bars), proteins (beef jerky), and then bread, fruit, veggies, etc. Nuts, for example, because of their fat content, have 50% more calories per pound than pure sugar.
Look at the lables. Choose foods you like, but choose the ones that are higher in calories for their weight. In that way, you get what you want, what your body needs for energy, and you keep it light. I usually plan for about 3000 calories a day. This isn't quite enough (I'm 6'3", 160 pounds), so I'll lose a pound or two on a weekend trip.
Bringing high-calorie foods like mixed nuts (2700/pound) and tortilla chips (2100/pound), I can get by with about 20 ounces of food per day. For a four day trip I'll carry around 5 pounds. Eat a big meal before you go, and you can carry less food (although you'll carry it inside you anyhow). You can cut weight if you know which berries to eat along the trail. I've eaten an entire meal of rasberries during one break while hiking in Colorado.
Healthy Backpacking Food
For a healthier trip, try this: Eat a large salad right before you leave, and right after you get back. If you also eat berries and herbs along the way, you can concentrate on bringing only light backpacking food, and your health won't suffer.
A more obvious alternative is to spend some money. Enough money, and you can feast on nutrition-packed, calorie-rich foods the whole time you are hiking. Try bee pollen, spirolina, raw nuts and seeds, molasses, dried papaya - I could go on, but you get the idea.
Finally, don't forget the freeze-dried meals and other traditional backpacking foods. They are not necessasrily healthy, and can be very expensive, but they sure are convenient and tasty. You can always pack ramen noodles if you want cheap food.