No. The second spell will replace the first.
However, if you create two weakness spells with different names but the same effect, then they will "stack".
Weakness it magic is more interesting. Because weakness to magic affects all magic. And Weakness to Magic is itself Magic.
So if you create a weakness to magic 100% spell and cast it twice, technically it does not stack because the second replaces the first. However the first will magnify the second. So casting that spell twice will give you 200% weakness to magic.
There is an alternative. If, in addition to mastery of Destruction, you also have mastery of Restoration; you can tack in a 5 second long Absorb Magicka element to your spell.
"Elemental Touch" - on touch spell.....
Weakness to Magic 100% x 6 seconds
Absorb magic 5 points x 6 seconds (will recoup 30 points but add only ?~a dozen points to your spell cost? ) (60+ points by double tapping the target

).
Cold 4 points x 2 seconds
Fire 4 points x 2 seconds
Lightening x 2 seconds
Absorb Health x 2 seconds
Damage Health x 2 seconds
Paralyze x 1 second
This is a suprisingly cheap spell, and the stacking of damage to itself with double and triple taps is very nice. The paralyze makes sure they don't fight back.