1. To sink or droop beneath some physical weight or burden. I began sagging under the all the bags I had to carry from the car to the train station. She sagged a bit under the weight of her fallen comrade, but she gritted her teeth and pushed onward.

2. To lose vigor or resolve because of something; to flag or weaken in spirits as a result of something. The whole team sagged under the news that our project was being canceled. I found myself sagging under the realization that all that hard work had been for nothing.