"Cast your burden upon the Lord and He will sustain you..." Psalm 55:22
It makes for really good preaching and sounds good when it is yelled from the pulpit, but I simply cannot believe that "God will not put more on you than you can bear." Practical experience and empirical evidence mitigate otherwise; God does put more on you than you can bear, and He is quite pleased to do so.
There are times in life when God places such a burden upon you so as to do a thing in your life; it is up to you to determine what that thing is and then accept it and live in it. That burden then becomes such a thing that God intends not to lift it from you so as to teach you that thing and further, to drive you to Him--to fall out of fellowship with Him because of the burden is a failure of an egregious sort and will only make the burden that much heavier to bear.
So to roll the responsibility upon God and allow Him to shoulder the heaviest portion of the burden is not only biblical but sound--it makes sense. The burdens we bear were never meant to be borne alone, yet what a celebration ensues when we do bear it alone! "I did this! I accomplished this thing!" But was any real lesson learned in faith? None whatsoever.
Can one be crushed under a heavy load? Quite possibly; but not if one end of the load has been deliberately given over to Him to shoulder.