A study of fat/skinny twins was only able to recruit 14 such twins from a registry of 2,453 twins. It doesn't say what fraction of those 2453 were fat/skinny ("obesity discordant"). The BMI ratio between those 14 was only 6/5.

They suggested that the obesity difference might be accounted for by mitochondrial DNA copy number. mtDNA copy number is regulated, not simply "genetically innate"; so I don't see that as a "genetic" explanation.

(I put "genetic" in quotes because the things we say have genetic causes are only a small subset of the things which have genes as causes.)

The researchers recruited 14 pairs of genetically identical Finnish twins born between 1975 and 1979 who were “obesity discordant”—that is, one twin of each pair had a BMI of about 25 (not obese); the other had a BMI of about 30 (obese). The researchers took fat and blood samples from each twin, determined the insulin sensitivity of each, and measured the body composition and various fat stores of each. They found that the obese twins had more subcutaneous, intra-abdominal, and liver fat and were less insulin sensitive than the non-obese twins. Insulin sensitivity correlated with the amount of liver fat. Analysis of gene expression in the fat samples showed that 19 gene pathways (mainly inflammatory pathways) were expressed more strongly (up-regulated) in the obese twins than the non-obese twins, whereas seven pathways were down-regulated. The most highly down-regulated pathway was a mitochondrial pathway involved in amino acid breakdown, but mitochondrial energy metabolism pathways were also down-regulated. Finally, mitochondrial DNA copy number in fat was reduced in the obese twins by nearly half, a novel observation that could partly account for the obesity-induced metabolic defects of these individuals.