A high sugar diet is more likely to affect your teeth or your waistline than your baby. I wouldn't worry about it.
Eating fatty foods may increase the fat content of a mom's milk... A little bit. Generally not enough to make a big difference in the amount of fat the baby gets. The type of fat that a mom eats (saturated vs. unsaturated) is thought to perhaps change the type of fat expressed in mom's milk- a mom who eats more plant-based (unsaturated) fats might make milk that contains more unsaturated fat, while a mom who eats more animal (saturated) fats may make milk that contains more saturated fats. (Reference: http://kellymom.com/nutrition/milk/change-milkfat/; same link PP posted). But none of this is a particularly big deal. You don't need to maintain a perfect or even particularly good diet in order to make good milk for your baby, and as the PP so rightly pointed out, breastfeeding burns a ton of calories and if you are hungry, there's a good reason why!
Coolest thing my big girl said recently: "How can you tell the world is moving when you are standing on it?"
Coolest thing my little girl sang recently: "I love dat one-two pupples!"