Is there a correlation between a person's birth weight and height at maturity?

Only a slight one.

The positive association between birth length and adult height was stronger than between birth weight and adult weight (R = 7-9% compared with <0.1%, respectively). The strongest associations were seen among those born at gestational age 39 to 41 weeks. The effects of birth length on adult height, and of birth weight on adult weight, were considerably less among preterm births than among term births. Length and weight at birth each contributed independently to adult stature and body weight. The increase in adult weight per relative birth weight category was greatest for infants who were both heavy and long at birth.

http://www.ncbi.nlm.nih.gov/pubmed/15703531