How to get combination results
SELECT  t1.weight,
        t2.weight,
        t3.weight,
        ...
        t12.weight
    FROM tbl t1
    JOIN tbl t2  ON t2.weight &gt; t1.weight
    JOIN tbl t3  ON t3.weight &gt; t2.weight
    ...
    JOIN tbl t12  ON t12.weight &gt; t11.weight
    WHERE t1.weight +
          t2.weight +
          t3.weight +
          ...
          t12.weight  = 296.35;


Possible issues:


What I provided does not allow for duplicate weights.  If that can happen, I need an id or something instead of weight for avoiding dups.
If you want the closest, not exact, match:


Replace the WHERE clause with something like:

    ORDER BY ABS( t1.weight + ... + t12.weight - 296.35 ) ASC
    LIMIT 1


This would probably run a lot faster in any programming language then SQL.

I worry that this query will not complete in my lifetime.  I think it would take billions, maybe trillions of iterations.

OR

The code above is "brute force".  With some more thinking, it should be possible to 'prune' the list to cut back significantly (down from trillions to billions??) the amount of work.  But that would need a recursive CTE (upgrade to MySQL 8.0) or, as I say, use a real programming language.