Albert Barnes Commentary Ezekiel 12:10

"Say thou unto them, Thus saith the Lord Jehovah: This burden [concerneth] the prince in Jerusalem, and all the house of Israel among whom they are." — Ezekiel 12:10 (ASV)

Burden - A word used to indicate a prediction of woe to be borne by some individual or people (Isaiah 13:1, note). Ezekiel, bearing his "stuff" on his shoulder, was a sign of the weight of calamity coming upon king and people.