In the marginal sea-ice zone (MIZ), where relatively small ice floes are dominant, floe-size distribution is an important parameter of the melting process because smaller ice floes are subject to stronger lateral melting due to their larger perimeters. However, the available data have been very limited so far. Analysis of sea ice in the Sea of Okhotsk revealed that while floe-size distribution is basically scale invariant, a regime shift occurs at a size of about 40 m. In order to extend this preliminary result to the Antarctic MIZ and further examine the controlling factors, the first concurrent ice floe size and ice thickness measurements were conducted in the northwestern Weddell Sea and off Wilkes Land (approximately 63.9° S, 116.8° E) with a heli-borne digital video camera in the late winter of 2006 and 2007. The floe sizes ranged from 2 to 100 m. Video images obtained every minute were used for analysis. Ice floes were extracted according to the brightness and the floe size was defined as the diameter of a circle that has the same area of the floe. Our analysis shows: (1) the scale invariance and regime shift are confirmed in both regions; (2) the floe size at which regime shift occurs slightly increases from 20 to 40 m with ice thickness, consistent with the theory of the flexural failure of sea ice; and (3) the aspect ratio is 1.6–1.9 on average, close to the previous results. Based on these results, the formation process of size distribution and its effect on the melting process are discussed. A renormalization group method was applied to explain the scale invariance in floe-size distribution for smaller floes by introducing a fragility of sea ice as a physical parameter. As a result, the fractal dimension was related to fragility and the importance of wave–ice interaction was elucidated to form the floe-size distribution.