Babyisaac - your mum can speak to the HVs and others at the clinic, and she will hear that 5 oz a week is a good average weight gain, and that to is very common for babies to 'catch down' to their 'natural' weight over the first weeks.
Someone will post here and say the charts are 'for formula fed babies' which is not true, as the charts are fine, and based on babies whose feeding is not differentiated. There is in any case not a great deal of difference between standard UK charts and the WHO charts which show breastfed babies only.
Beyond the first few months, though, standard UK charts apply less and less to breastfed babies, as the 'breastfed only' charts show babies from that age slowing down their weight gain.
The issue is, I'm afraid, with people who think weight is the be-all and end-all of infant health, which as you suspect is quite wrong.
In fact, babies who are heavier than they are meant to be could be storing up problems in the future.
What a shame your mum can't support you in your breastfeeding and share your joy in the health and happy development of your son. If she is 'always' saying 'put him on bottles' then yes, I do think she is bullying, and she needs to stop it. Perhaps a frank discussion with her in which you explain how disturbing and upsetting she is being will help you now and in the future.