Introduction: While the genetic and environmental underpinnings of body weight and alcohol use are fairly well-known, determinants of simultaneous changes in these traits are still poorly known. We sought to quantify the environmental and genetic components underlying parallel changes in weight and alcohol consumption and to investigate potential covariation between them. Methods: The analysis comprised 4,461 adult participants (58% women) from the Finnish Twin Cohort with four measures of alcohol consumption and body mass index (BMI) over a 36-year follow-up. Trajectories of each trait were described by growth factors, defined as intercepts (i.e., baseline) and slopes (i.e., change over follow-up), using latent growth curve modeling. Growth values were used for male (190 monozygotic pairs, 293 dizygotic pairs) and female (316 monozygotic pairs, 487 dizygotic pairs) same-sex complete twin pairs in multivariate twin modeling. The variances and covariances of growth factors were then decomposed into genetic and environmental components. Results: The baseline heritabilities were similar in men (BMI: h<sup>2</sup> = 79% [95% confidence interval: 74, 83]; alcohol consumption: h<sup>2</sup> = 49% [32, 67]) and women (h<sup>2</sup> = 77% [73, 81]; h<sup>2</sup> = 45% [29, 61]). Heritabilities of BMI change were similar in men (h<sup>2</sup> = 52% [42, 61]) and women (h<sup>2</sup> = 57% [50, 63]), but the heritability of change in alcohol consumption was significantly higher (p = 0.03) in men (h<sup>2</sup> = 45% [34, 54]) than in women (h<sup>2</sup> = 31% [22, 38]). Significant additive genetic correlations between BMI at baseline and change in alcohol consumption were observed in both men (rA = −0.17 [−0.29, −0.04]) and women (rA = −0.18 [−0.31, −0.06]). Non-shared environmental factors affecting changes in alcohol consumption and BMI were correlated in men (rE = 0.18 [0.06, 0.30]). Among women, non-shared environmental factors affecting baseline alcohol consumption and the change in BMI were inversely correlated (rE = −0.11 [−0.20, −0.01]). Conclusions: Based on genetic correlations, genetic variation underlying BMI may affect changes in alcohol consumption. Independent of genetic effects, change in BMI correlates with change in alcohol consumption in men, suggesting direct effects between them.