I agree with the mental health stuff. I once was struggling with life so much that all I had energy for was to turn up to work, come home sleep. I didn't shower, brush my teeth, cook, clean, shop, anything, for days at a time. Someone came over and was like you really smell, you need to shower and shampoo your hair, and brush your teeth so bad!
I ended up getting counseling and antidepressants but it was really depressed during that time of my life without realising it

Sorry to hear this, he needs to shower though that's just basic life skills. If someone hasn't showered 2 times a day, especially in this sweaty country, there is no way I'm rooting you regardless of how skinny or fat you are.

I'm an over weight woman and like your husband I can smell up really quickly.
However I am conscious of this, overly. He may not smell himself and may have other issues that you are unaware of.
For example- does he have any skin issues that could deter him from showering? When my dermatitis flares up, showering is incredibly painful hence not wanting to shower.

My husband has put on a lot of weight too and whilst I think he could lose weight if he wanted to, I give him the benefit of the doubt. If he stopped showering I would leave. This is clearly within his control, stop babying him.

Clearly some mental health stuff going on here. Support him to go and see a psychologist to work out what's happening between the ears.