Seed plants vary tremendously in size and morphology. However, variation and covariation between plant traits may at least in part be governed by universal biophysical laws and biological constants. Metabolic Scaling Theory (MST) posits that whole-organismal metabolism and growth rate are under stabilizing selection that minimizes the scaling of hydrodynamic resistance and maximizes the scaling of resource uptake. This constrains variation in physiological traits and in the rate of biomass accumulation, so that they can be expressed as mathematical functions of plant size with near constant allometric scaling exponents across species. However, observed variation in scaling exponents questions the evolutionary drivers and the universality of allometric equations. We have measured growth scaling and fitness traits of 451 Arabidopsis thaliana accessions with sequenced genomes. Variation among accessions around the scaling exponent predicted by MST correlated with relative growth rate, seed production and stress resistance. Genomic analyses indicate that growth allometry is affected by many genes associated with local climate and abiotic stress response. The gene with the strongest effect, PUB4, has molecular signatures of balancing selection, suggesting that intraspecific variation in growth scaling is maintained by opposing selection on the trade-off between seed production and abiotic stress resistance. Our findings support a core MST prediction and suggest that variation in allometry contributes to local adaptation to contrasting environments. Our results help reconcile past debates on the origin of allometric scaling in biology, and begin to link adaptive variation in allometric scaling to specific genes.