Inhibits the Wnt/Wingless pathway by binding to CTNNB1/beta-catenin and inhibiting beta-catenin-mediated transcriptional activation through competition with TCF/LEF transcription factors. Has also been shown to play a role in regulating the intracellular trafficking of polycystin-2/PKD2 and possibly of other intracellular proteins. Promotes adipocyte and cardiomyocyte differentiation. Homodimer. Interacts with polycystin-2/PKD2 and GM130. Interacts with the C-terminal region of CTNNB1. Interacts (C-terminus) with TCIM (C-terminus), TCIM competes with CTNNB1 for the interaction with CBY1. Interacts with FAM92A; this interaction facilitates targeting of FAM92A to cilium basal body. Interacts with CIBAR2. Nuclear, in a punctate manner (By similarity). 'Chibby' is Japanese for 'small'; the gene was so named for the RNAi phenotype seen in flies. Belongs to the chibby family.