Does metal under low tension ever actually bend? Let's assume something like a pair of tweezers, since that's strangely what led to this mental exercise.
Does the metal ever actually permanently transform its shape? Stainless steel is fairly malleable, but in this case even with tweezers held closed, is there ever a point where removing this constriction would result in no change in shape (i.e they stay closed permanently until bent back)? Is there a mathematical way to define how long this would take? Would it simply stay in tension forever unless more force was added to reshape the metal?
 A: I would guess you're thinking about the phenomenon called creep.
Your piece of metal is made up from crystals in which each atom has a well defined position with respect to the atoms around it, and it takes a lot of energy to make an atom jump completely out of its position. When you elastically deform the metal you displace atoms very slightly, but when you release the metal the atoms return to their equilibrium positions and the metal returns to its original shape. Permanent deformation happens when you apply so much force that it makes some of the atoms jump completely out of their original locations and into new positions.
However even under small deformations it is possible for atoms to move causing the deformation to become permanent. Metals generally contain defects in their crystal structure called dislocations and the atoms near a dislocation are generally more mobile than atoms in the rest of the metal. Under even small applied forces movement of atoms at a dislocation can cause the dislocation to move and the metal to permanently deform.
Alternatively, at any temperature above absolute zero the atoms in a metal have some thermal energy so they are vibrating about their equilibrium positions. As you increase the temperature the atoms vibrate more and this makes it easier for them to move. The obvious extreme example of this is melting, where the atoms vibrate so much it breaks down the regular crystal lattice and becomes a liquid. However even below the melting point increased temperature can allow atoms to move and this can cause a small deformation to become permanent.
To what extent creep happens, and how fast, depends on the type of metal and how the metal has been treated. Obviously your tweezers are designed to be flexible and will have been made from a metal that does not creep readily.
A: Low tension is relative.  In the range a metal (or other material will) returns to the original shape once an external force is removed is called the elastic range.  If you stress the material past the yield point it will plasticly deform.  In plastic deformation it just plain bends - it will snap back a little but not to the original shape.  If you apply enough stress it it will fail (as in fracture).  A tweezers is design for a good elastic range.  But it will have a very narrow range between plastic deformation and failure.  
Not really the question but as you stress a material in the elastic range it will fatigue and eventually develop fatigue cracks.  Some material fatigue at higher rates.   If you cycled the tweezers a million times you might get a fatigue crack.
Lets say you did bend it.  Bending it back is not the same.  You cannot readily get back the original micro structure.  If it was heat treated then that is basically gone. 
