Yes, of course they do. Adult hummingbirds are small, and no, they'll never get bigger once they reach adulthood--like any animal. But a a hummingbird egg is even smaller--the size of a small jellybean or pea--and the babies weigh the fraction of the weight of a US dime.
Here's an article about the birth and growth of baby hummingbirds, if you're really curious. It even has pictures--which are hard to find!
Oh yes they do and it is beautiful! I saw a hummingbirds nest in my apartment complex they were SUPER tiny when they were born, the nest was tiny too. The mother was scared away by these mean teenage guys so ME and my friend took care of them and watched them fly away. They grow, and it's a really beautiful sight.