The culmination of solar cycle 24 by the end of 2019 has created the opportunity to compare the differing properties of coronal mass ejections (CMEs) between two whole solar cycles: solar cycle 23 (SC 23) and solar cycle 24 (SC 24). We report on the width evolution of limb CMEs in SCs 23 and 24 in order to test the suggestion by Gopalswamy et al. that CME flux ropes attain pressure balance at larger heliocentric distances in SC 24. We measure CME width as a function of heliocentric distance for a significantly large number of limb CMEs (~1000) and determine the distances where the CMEs reach constant width in each cycle. We introduced a new parameter, the transition height (hc) of a CME, defined as the critical heliocentric distance beyond which the CME width stabilizes to a quasi-constant value. Cycle and phase-to-phase comparisons are based on this new parameter. We find that the average value of hc in SC 24 is 62% higher than that in SC 23. SC 24 CMEs attain their peak width at larger distances from the Sun than SC 23 CMEs do. The enhanced transition height in SC 24 is new observational ratification of the anomalous expansion. The anomalous expansion of SC 24 CMEs, which is caused by the weak state of the heliosphere, accounts for the larger heliocentric distance where the pressure balance between CME flux rope and the ambient medium is attained.