Slitherine

When I go to my nation panel, I see I am losing two wars.

It is true that two fairly weak neighbors declared war on me, but the one battle I fought against the one was an easy slaughter. No one has so much as reduced one of my unit's effectiveness by a single point. The main thing restraining me is that I don't want their crappy territory.

I know that I am stuck with the two points of war weariness every turn, but is there actually any penalty being inflicted by this warning that I am losing two wars? Any hit on morale or loyalty?

No, its indicative and someitmes, esp for small wars a bit misleading. I think its making a strength comparison and it assumes you should be doing better.

There may be a hit if you are Rome as a Republic or Carthage - this may affect the popularity of your current ruling faction