The associations between maternal pre-pregnancy obesity and low birth weight (LBW, <2500 g) remain inconclusive. Therefore, birth weight in a Polish prospective cohort of 912 mothers was investigated depending on the pre-pregnancy body mass index (BMI). The whole cohort and the subgroup of gestational weight gain (GWG) in the range of the Institute of Medicine (IOM) recommendations, as well as ‘healthy’ women (who did not develop diabetes or hypertension in this pregnancy) were investigated. Adjusted odds ratios (AOR) of the newborn outcomes (with 95% confidence intervals, CI) for obesity (BMI ≥ 30 kg/m2) vs. normal BMI (18.5−24.9 kg/m2) were calculated using multiple logistic regression. Risk profiles (in the Lowess method) were presented for BMI values (kg/m2) and threshold BMI values were calculated. (1) In the cohort, LBW affected 6.6% of pregnancies, fetal growth restriction (FGR) 2.3%, and macrosomia 10.6%. (2) The adjusted risk of macrosomia was more than three-fold higher for obesity compared to normal BMI in the whole cohort (AOR = 3.21 (1.69−6.1), p < 0.001) and the result was maintained in the subgroups. A 17-fold higher adjusted LBW risk for obesity was found (AOR = 17.42 (1.5−202.6), p = 0.022), but only in the normal GWG subgroup. The FGR risk profile was U-shaped: in the entire cohort, the risk was more than three times higher for obesity (AOR = 3.12 (1.02−9.54), p = 0.045) and underweight (AOR = 3.84 (1.13−13.0), p = 0.031). (3) The risk profiles showed that the highest BMI values were found to be associated with a higher risk of these three newborn outcomes and the threshold BMI was 23.7 kg/m2 for macrosomia, 26.2 kg/m2 for LBW, and 31.8 kg/m2 for FGR. These results confirm the multidirectional effects of obesity on fetal growth (low birth weight, fetal growth restriction, and macrosomia). The results for LBW were heavily masked by the effects of abnormal gestational weight gain.