A striking global health development over the past few decades has been the increasing prevalence of overweight and obesity. At the same time, depression has become increasingly common in almost all high-income countries. We investigated whether body weight, measured by body mass index (BMI), has a causal effect on depression symptoms in Finland. Using data drawn from the Cardiovascular Risk in Young Finns Study (N = 1,523, mean age 41.9, SD 5), we used linear regression to establish the relationship between BMI and depression symptoms measured by 21-item Beck’s Depression Inventory. To identify causal relationships, we used the Mendelian randomization (MR) method with weighted sums of genetic markers (single nucleotide polymorphisms, SNPs) as instruments for BMI. We employ instruments (polygenic risk scores, PGSs) with varying number of SNPs that are associated with BMI to evaluate the sensitivity of our results to instrument strength. Based on linear regressions, higher BMI was associated with a higher prevalence of depression symptoms among females (b = 0.238, p = 0.000) and males (b = 0.117, p = 0.019). However, the MR results imply that the positive link applies only to females (b = 0.302, p = 0.007) but not to males (b = -0.070, p = 0.520). Poor instrument strength may explain why many previous studies that have utilized genetic instruments have been unable to identify a statistically significant link between BMI and depression-related traits. Although the number of genetic markers in the instrument had only a minor effect on the point estimates, the standard errors were much smaller when more powerful instruments were employed.