1.weigh (someone or something) down or weigh down (someone or something) : to press down on (someone or something) : to make (someone or something) heavier and less able to move easily

• My heavy backpack weighed me down.
• The boat was weighed down by the extra cargo.

2. weigh (someone) down or weigh down (someone) : to cause (someone) to accept or deal with something difficult or unpleasant

• I don’t want to weigh you down with my bad news.
• I’m feeling weighed down[=burdened] by all the work I have to do.