One of the most celebrated achievements in polymer physics is the finding of simple scaling laws that correlate molecular behaviors with molecular size. Scaling relations of 2D macromolecules between the conformation and size have been extensively investigated in theory. However, in contrast to their 1D counterparts, the fundamental correlation of conformation with the size, bending rigidity, and surface interaction still remains unsolved in both experiments and theory. Here we report the scaling relations of 2D macromolecules by using single-layer graphene oxide as the model, underpinning a general framework to understand and measure their thermodynamic and rheological behaviors. Using Ubbelohde capillary rheology, we experimentally determined the Flory-type and Mark-Houwink-Sakurada scaling rules in the self-avoiding, good-solvent regime through the critical overlapping concentration (C-* similar to L-0.87, L is the lateral size) and intrinsic viscosity ([eta] similar to M-alpha, alpha = 0.33, M is the molecular weight). The measured exponent gamma = 0.87 is well located between self-avoiding (4/5) and rigid (1) limit, indicating a nearly flat conformation and semiflexible nature, and alpha = 0.33 differs from the value of polymers (0.5-0.8), signaling the dimensional constraint. The discussion of conformational size-scaling relations is complemented by dissipative particle dynamics simulations, which clarify the effects of size and bending resistance of 2D macromolecules as well as the solvent that tunes their surface interaction, resulting in conformation transitions among nearly flat, folded, and crumpled phases.