Rant away! Your dp hasn't handled the situation well.
But after you've calmed down a bit, I really would consider working out a shared strategy to ensure you help your DD navigate a world with an incredibly unhealthy attitude towards beauty, body image, women, weight, fat, health, guilt, blame, and personal responsibility.
Because your dd will be hearing and influenced by cultural values and messages from many different sources, even at 5 yrs old.
I'd question the banning of words and the avoidance of subjects altogether. That means your voices aren't heard in a sea of other people's voices, and media, society in generals.
Banning words in the long term can have the opposite effect from minimizing or dismissing what she will see with her own eyes and hear with her own ears outside the home.
Laying down a blanket of silence creates an atmosphere where fat is loaded with even more strength and intensity, which could be diffused if they were less taboo and less emotionally loaded.
So unless it's to intervene in a harmful situation as the one Somerville mentions, then I'd seriously reconsider the outcome of giving this word such power... Being overweight should never be seen as being 'so bad it has no name'.
It's up to us to show our children that fat is just fat, and shouldn't be so awful it cannot be spoken about... Remember the whole 'He Who Should Not Be Named' thing in Harry Potter?!
And if you can forgive me quoting JK Rowling...
There was an ace TED talk on the increasing need for parents / families to be increasingly vocal and explicit about their own values and attitudes to life, to act as a counter balance to the overwhelming amount of (unhealthy/ negative) loud messages and persuasion children are exposed to everyday. That parents cannot rely on their children absorbing positive and healthy values and attitudes just by osmosis... and the necessity of parents having to be very visible and loud to teach their own values in a world where so many other messages are bombarding our children day in day out. And how maintaining a dignified silence is a very risky strategy, as it doesn't actively help children navigate such a difficult landscape, and it allows children especially as they enter their teens to drift away towards the louder siren call of unhealthy /dangerous affiliations etc.