My baby was 6 weeks premature and weighs much less than a term baby his age. Should I wait to get vaccinated?

Hi there. My baby was born 6 weeks premature weighing only 3 pounds 5 ounces. He is 3 months old today but doesn't weigh anywhere near as much as a term 3 month old baby. Should I get his shots based on his weight instead of age? I'm already weary about giving him shots but if I do get him vaccinated I don't want them giving his 4 month shots when he is not the size of a term newborn. What do you think? All input is appreciated.