Pleiotropic effects of mutations underlie diverse biological phenomena such as ageing and specialization. In particular, antagonistic pleiotropy (“AP”: when a mutation has opposite fitness effects in different environments) generates tradeoffs, which may constrain adaptation. Models of adaptation typically assume that AP is common - especially among large-effect mutations - and that pleiotropic effect sizes are positively correlated. Empirical tests of these assumptions have focused on de novo beneficial mutations arising under strong selection. However, most mutations are actually deleterious or neutral, and may contribute to standing genetic variation that can subsequently drive adaptation. We quantified the incidence, nature, and effect size of pleiotropy for carbon utilization across 80 single mutations in Escherichia coli that arose under mutation accumulation (i.e., weak selection). Although ~46% of the mutations were pleiotropic, only 11% showed AP; among beneficial mutations, only ~4% showed AP. In some environments, AP was more common in large-effect mutations; and AP effect sizes across environments were often negatively correlated. Thus, AP for carbon use is generally rare (especially among beneficial mutations); is not consistently enriched in large-effect mutations; and often involves weakly deleterious antagonistic effects. Our unbiased quantification of mutational effects therefore suggests that antagonistic pleiotropy may be unlikely to cause maladaptive tradeoffs.