Weight, diet, exercise levels and the misconceptions around them are hugely emotive. It isn't as straightforward as calories in vs calories out no matter how much some people would like it to be.
Yes, if you eat less and move more you should lose weight. But you may lose less weight with the same percentage calorie reduction and activity increase than your friend. There are genetic components, there are individual metabolic components and there is the huge unknown of your microbiome which has a far greater role to play than people realise.
Case study - mother and child. Similar lifestyle and genetics. Mother overweight/obese, child slim. Child became ill with something requiring fecal transplant (yes this is a thing). Mother used as donor, child's gut repopulated with maternal biome. Child completely recovers and returns to original lifestyle (same dietary intake and exercise levels). Child slowly gains weight until she is the same level of overweight as her mother.
The gut bacteria have a huge role to play in processing the food you eat. Slimmer people tend to have a larger proportion of good bugs, overweight people have a higher proportion of the bad bugs. But whether a high sugar diet encourages the bug imbalance, or whether fatter people are populated with more of the bad bugs during their embryonic growth & birth (from their mother which makes the above case study even more interesting) - so much is not known.
On the whole though - back to size being emotive - generally, if someone says they barely eat but are still gaining weight or failing to lose it, there is secret eating / denial / guilt going on somewhere. Yes medical conditions can make weight gain easier (steroids make you hungry, pain makes it harder to move) and weight loss harder, but I would think OP's mum is secretly eating somewhere. I don't think she's doing it for attention though. I think she's probably trying to hide it out out of guilt, so drawing attention to how little she eats and desperately ignoring her food intake when alone.