bend/lean over backward, to

lean over backward

To expend a lot of energy or effort to do something; to inconvenience oneself. I can't believe how ungrateful you're being, especially since we leaned over backward planning this dinner party for you! Please don't lean over backward preparing for my visit—I'm totally prepared to sleep on your floor!
See also: backward, lean, over

bend/lean over backward, to

To exert oneself enormously, to go to a great deal of trouble to satisfy or please someone. Originating in the United States about 1920, this expression, with its image of straining to do a backbend, is well on its way to cliché status.
See also: bend, lean, over

lean over backward

See bend over backward.
See also: backward, lean, over