What do you think Wordsworth meant by "the burden of the mystery" in line 39 of "Lines Composed a Few Miles Above Tintern Abbey"?

Wordsworth's line brings to mind the ideals of the Romantic movement, where Wordsworth was a main player. Specifically, when Wordsworth finds that the view before him relieves the "burden of the mystery," he is hearkening to the ideal of the "sublime," where Romantics found peace in the beauty of nature: 

                that serene and blessed mood, 
In which the affections gently lead us on,— 
Until, the breath of this corporeal frame 
And even the motion of our human blood 
Almost suspended, we are laid asleep 
In body, and become a living soul: 
While with an eye made quiet by the power 
Of harmony, and the deep power of joy, 
We see into the life of things. (39-47)

Going along with the Romantic ideals, Wordsworth's definition of burdens would be unique to the individual.  He speaks earlier in the poem about those in the village he imagines; those individuals would have their own burdens—work, children, enemies, and so on. The Hermit that he mentions in lines 21-22 might have more intellectual burdens, perhaps thinking about the mysteries of life and death.  For these individual reasons, Wordsworth does not define those burdens; he wanted to make his own personal remembrances of Tintern Abbey and River Wye accessible to anyone reading his lines.  That was another aspect of Wordsworth that made him famous—the ease with which anyone could read and understand his writing.

Long after he saw the wonders of nature along the river Wye, Wordsworth credits his memory of "these forms of beauty" (line 24) with "tranquil restoration" (line 31). In other words, just thinking about these sights can restore his peace of mind. He also credits these memories with "another gift," (line 37), which is the mood

In which the burthen of the mystery,
In which the heavy and the weary weight
Of all this unintelligible world
Is lighten'd (lines 39-42).

In other words, when Wordsworth recalls the peacefulness of these scenes from nature, which he saw five years before, the mystery of our existence and the burden this mystery places on us become lighter. He no longer struggles with the questions that plague him about life and its meaning; instead, he is able to be at peace. "The burthen of the mystery" is Wordsworth's poetic way of referring to everything people question about life. They are burdens because our purpose and meaning pose unanswerable questions.