You can stop worrying, Krystle. Your son sounds like a normal toddler to me. Avoiding meat is common at this age, and the protein requirements can be met though other food groups.
Your son's weight is within the acceptable range for his age, but his pediatrician can show you his actual growth patterns. Also, because he was premature, he may still be catching up. If he isn't losing weight, he's eating enough calories to grow on. We have to remember that our children eat very small portions. There are certain times in those early years when their energy requirements decrease because they are not growing as rapidly as they did as babies.
The taste buds in small children aren't very mature yet, although we are born with the ability to taste sweet and sour. As long as the foods you serve don't contain corn syrup or added sugars as a main ingredient, I would be patient until he can distinguish different tastes more easily.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.