The Weibull size effect, consisting of an increase in fracture strength with decreasing specimen size, constitutes the basis of the probabilistic design of brittle structures. Here we present evidence of a reverse size effect in submicron amorphous carbon films. Underlying this effect is the presence of critical defects of comparable size in all films. This leads to higher stress intensity factors, and concomitant decrease in strength, with decreasing thickness. The results have implications concerning the mechanical reliability of submicron scale devices.