I think the thing is, that if he's not ill enough to really hammer the GP about looking into it more, it's hard to gauge how unwell he really is.
We all know a lot of people who never feel great it seems, but don't do anything about it and don't have the best lifestyles. Cliche as it is, fresh air and mild exercise helps when you feel unwell. Vegetating on the sofa, does not (unless you are so ill, you literally can't do anything else, but is that the case?)
I also think that is hard to sympathise when it goes on for years and he's not pulling his weight as a result. When I feel unwell (and many other women I know), I still do all the house work, go to work, pump myself up to engage and do things outside with the kids, etc etc. I only stop doing these things when I literally can't get out of bed, so unwell. So he can feel "not great", but that doesn't mean he can't do any chores.
And if I felt so bad that I couldn't get up once a week, I'd take it pretty serious and would want it taken seriously by the doc too.
Also, as other posters have pointed out, you can sympathise and help him, but you're not his mum. Essentially, if this is something serious that is affecting him and you by extension, it's his responsibility to look after himself as well as possible and get to the bottom of it, if possible, to help you both, rather than just not do anything at all.