The fact that you remain standing or lying in one place—not crashing through the floor—means that your weight is opposed by forces generated by the floor or mattress. The gravitational potential energy of your body thus remains constant and energy is conserved in that sense.
When your muscles do work, such as lifting weight, chemical reactions in muscle cells generate large pushing or pulling forces—the energy source is chemicals derived from food. The strength of these forces is not related to body weight per se, though natural selection tends to give animals (including homo sapiens) the muscle power they need but no more.
You stand up, instead of collapsing into a heap at your feet, because the various muscles in your body hold you upright. I’m no expert on body mechanics, but I know that some muscle attachments work as 3rd class levers—trading speed for force. This means that the muscle must generate larger forces than the resistance to be opposed, in order to move through a large arc, analogous to pushing a door near its hinges.
Perhaps our ancestors needed the ability to jump, which certainly requires forces exceeding body weight. Also, mothers who carry offspring use leg and back muscles that bear their combined weight even when standing still.