Because of the amount of loss of minerals from rain, wind, erosion, etc. it's best to compost your weeds/plants in place as much as possible (see Masanobu
Fukuoka methods).
However, second best option is to compost and return all vegetation from your property to your property - as your doing.
As for your thought for the day question, seems defeating to wait in order to remove more minerals here, only to add to compost, and then to return it to there - IMO.
Pull weeds only as a last resort, and then in the easiest possible way - like when they are small, the ground is damp, and such. Or better yet get some white vinegar and spray them in place being careful not to spray anything you want to keep. I often use a piece of
cardboard in the spring to block/push back plants I want and easily spray the little weeds in-place.
You want your
land working for you and not the other way round, as much as possible.