A heavy load.

A responsibility, onus.

A cause of worry; that which is grievous, wearisome, or oppressive.

To encumber with a literal or figurative burden.

“to burden a nation with taxes”

To impose, as a load or burden; to lay or place as a burden (something heavy or objectionable).

The tonnage of a ship based on the number of tuns of wine that it could carry in its holds.