Can’t say much about anyone else, but even without the weight gain element, monster girls have the advantage of being people but “different”. and the “different” has a lot of options. Monster musume has that being more about cultural differences, with a lower dose of the large scale differences of their “monster/animal” type- like reptilian monstergirls being cold blooded or centaurs being vegetarian like horses. On the other hand, Inteviews with monster girls focused on the more “human” monster girls and used them as standins for more everyday disabilities and hangups, but exaggerated. Like vampirism being more like Albinism with regards to the sun, or the Yuki-onna’s “Icy” persona being about social anxiety.
But beyond the possibilities, monstergirls have the advantage of being “human” in ways that anthros tend not to be. Most monstergirls tend to “human with animal bits stapled on”- like a mermaid is a human woman who’s legs have been replaced with a fish tail. or a “catgirl” being a woman with a floofy tail and ears to scritch in a best of both worlds situation. the general concept of human is still there, there are just some dfferences around the extremities. In contrast, going full anthro tends towards taking an animal and modifiying humanity to it- like the distinction between a catgirl being a human woman with floofy ears and tail, vs having an entirely fur coated bipedal body and kitty snoot but with human breasts. so the distinction here would be like Darkstalker’s catgirl Felicia vs the general concept of a werewolf. Felicia reads much more human, even though she is also a kitty to scritch behind the ears and has a floofy tail