Foetal birth weight is an important determinant of perinatal health. For this reason, various methods have been investigated for estimating this weight during pregnancy. The aim of this study is to evaluate the possible relationship between full-term birth weight and pregnancy-associated plasma protein-A (PAPP-A) levels determined during the first trimester as part of combined screening for aneuploidy carried out in pregnant women. We carried out a single-centre study including pregnant women who were being followed up by the Obstetrics Service Care Units of the XXI de Santiago de Compostela e Barbanza Foundation, who gave birth from March 1, 2015, to March 1, 2017, and who had undergone their first-trimester combined chromosomopathy screening. The sample included a total of 2794 women. We found a significant correlation between MoM PAPP-A and foetal birth weight. When MoM PAPP-A was measured at extremely low levels (< 0.3) during the first trimester, the OR for giving birth to a foetus with weight < p10, adjusting for gestational age and sex, was 2.74. For low levels of MoM PAPP-A (0.3–0.44), the OR was 1.52. With regard to the value of MOM PAPP-A levels as a predictor of foetal macrosomia, a correlation could be observed with elevated levels, although this was not statistically significant. PAPP-A determined during the first trimester acts as a predictor of foetal weight at term as well as for foetal growth disorders.