When the weather is hot and humid, my eye sight worsens. Is this normal?

Not really. Eyesight should not vary by humidity or temperature (unless your glasses fog up!). Generally, if the vision does decrease as you mentioned, you should see an eye doctor; there are certain eye conditions that can be causing your symptoms. Your doctor can diagnose the cause and discuss treatment options to help improve your vision.
No. Hot humid weather can make fuchs' dystrophy worse - this is a condition where the cornea swells and becomes cloudy. Also, if you have blepharitis or irritation of the oil glands in the lids, hot weather can exacerbate this. Lastly, you may have multiple sclerosis - these patients often don't do well in the heat. Best to be checked out.