Re: Gaining to fast?
No, you cannot overfeed a breastfed baby, because you are not in charge of feeding him. He's in charge of feeding himself! A breastfed baby learns to identify his satiation cues and stop nursing when he is full. This is totally different from the way a baby eats from the bottle; bottlefed babies are routinely overfed because the adult is in charge of the feeding, and even the most sensitive bottle-feeding parent may tip the bottle up to get the baby to take food in faster, or may replace the bottle in the baby's mouth to encourage him to finish "the last little bit."
It's normal for breastfed babies to gain extremely rapidly in the first few weeks/months of life. As much as a pound a week is common! The baby's rate of weight gain will slow down as he gets into his second six months, and many breastfed babies start to drop percentiles as they become more mobile and devote increasing amounts of calories to action, rather than packing them on as fat. For example, my second kid gained a pound a week for the first month or two, going from around the 40th %ile at birth to the 100th %ile at 2 months. By 6 months she was down to the 80-85th %ile.
If you're worried that your baby is going to end up too fat to move, don't be! Just enjoy the chub while it lasts, because a lean toddler will emerge by the end of your baby's first year.
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!"