Weakness to Sunlight works on several options: one could either have their monster powers greatly diminished, or have their physical strength weakened. Or they may go for the third option with burning on contact with sunlight.
In all cases, a character would need to be in a covered/protected vehicle to avoid activating that trait during the daylight. Cloudy skies would reduce this to a degree (example: a character would feel a burning sensation in their skin rather than bursting into flame, or be strong enough to lift their own weight or use a power at half strength.) Clothing would not provide much in the way of protection.
Re: monster question
In all cases, a character would need to be in a covered/protected vehicle to avoid activating that trait during the daylight. Cloudy skies would reduce this to a degree (example: a character would feel a burning sensation in their skin rather than bursting into flame, or be strong enough to lift their own weight or use a power at half strength.) Clothing would not provide much in the way of protection.