Many scientific questions require estimating the effects of continuous treatments. Outcome modeling and weighted regression based on the generalized propensity score are the most commonly used methods to evaluate continuous effects. However, these techniques may be sensitive to model misspecification, extreme weights or both. In this paper, we propose Kernel Optimal Orthogonality Weighting (KOOW), a convex optimization-based method, for estimating the effects of continuous treatments. KOOW finds weights that minimize the worst-case penalized functional covariance between the continuous treatment and the confounders. By minimizing this quantity, KOOW successfully provides weights that orthogonalize confounders and the continuous treatment, thus providing optimal covariate balance, while controlling for extreme weights. We valuate its comparative performance in a simulation study. Using data from the Women’s Health Initiative observational study, we apply KOOW to evaluate the effect of red meat consumption on blood pressure.