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to hang over; to cover
to fall upon someone (responsibility, burden, pressure, etc.)
重い雲が山全体に覆い被さった。
Heavy clouds hung over the entire mountain.
大木が道に覆い被さって通行を妨げていた。
A large tree hung over the road, blocking traffic.
霧が街全体に覆い被さるように低く垂れ込めていた。
The fog hung low as if covering the whole town.