Welcome to the world of being a poop obsessed bunny parent! I think there are a lot of us here haha.
I think giving a little watery critical care when you notice something is just slightly off is perfectly fine and a great thing to do (I do the exact same thing with my bunnies). The only time I wouldn’t is if you really suspect a severe blockage or bloat (like you notice a large chunk of foreign material was eaten, or something like that).
To answer your question about stress, it kind of depends on the bunny, but probably not too much. I think that they can pick up on our stress, but the type of stress causing small poops is usually something much more stressful (like perhaps a trip to the vet or maybe a loud dog barking outside for a long time).
Have you had his teeth examined? Lops are somewhat prone to dental issues, so that could be influencing his hay-eating (and poop size).
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.