[LunaTheHamster1]

I'm not an expert on dwarf hamsters, and I think that is what you have going by your pic and the weight. Weight can vary so much and i think it is rather a case of if a hamster maintains their weight, that generally is a good sign of the amount of food and the type of food they are eating is doing what it should for them. 120g did sound a lot, but 70g sounds about right to me. My robo is approx 34-36g and dwarfs are roughly twice the size of him. But, again I know some robos will only weigh about 19g. so they can vary.
Is your mum looking at syrian hamster weights. Because they can weigh anything from around 130g to 300g depending on their size and if been ethically bred etc.
If you are giving your hamster healthy treats like leafy greens and his normal food I think you will be on the right track. Yes, sadly pet stores aren't the best place to look for hamster items, although you really think they would be. Things like empty tissue boxes or empty crisp tubes can work really well too and don't cost a fortune.