Christ's burden is knowledge of the truth

25At that time Jesus answered and said, I thank thee, O Father, Lord of heaven and earth, because thou hast hid these things from the wise and prudent, and hast revealed them unto babes. 26Even so, Father: for so it seemed good in thy sight. 27All things are delivered unto me of my Father: and no man knoweth the Son, but the Father; neither knoweth any man the Father, save the Son, and he to whomsoever the Son will reveal him.

28Come unto me, all ye that labour and are heavy laden, and I will give you rest. 29Take my yoke upon you, and learn of me; for I am meek and lowly in heart: and ye shall find rest unto your souls. 30For my yoke is easy, and my burden is light.

 - Matthew 11

"Light" here is taken to mean knowledge and not some sort of weight. Christ is the radiance and glory of God and has revealed his truth to man. He is therefore said to be the light of the world. He is not dark but light and in him does the fullness of deity dwell. Of course in context 28 comes after 27.