Why do the wings bend and flex?

They're meant to. Wings are built to flex, a bit like a car's suspension soaking up bumps. US certification rules require an airliner's structure to carry its maximum expected loads without harmful permanent deformation, and say that any bending up to those loads must not interfere with safe operation.¹ On long-range jets you may see the wingtips rise noticeably in flight. That's normal and expected.