This isn't normal workout type breathing. It's very, very VERY loud and it's constant. I get that he cannot help how he breathes. Wish I could post an audio link so you'd know what I'm saying.
The grunting with the weight lifting isn't like "ooh this is heavy" - it's breathing AND grunting with every rep he does, both up and down. I can't describe it. But I know it also bothers my spouse when he comes with me.
With this update, it sounds like he can't help either version of the noise, so yeah, headphones.