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Sorry for the beginner question.
I was wondering if the Spell "Magic Weapon" would make a +1 keen longsword into a +2 keen longsword for the duration of the spell.
or does it only work on nonmagic weapons?
Magic Weapon creates an enhancement bonus.
the +1 on a magic sword is also an enhancement bonus.
Bonuses from the same source do not stack, they overlap.
So, casting magic weapon on a +1 keen longsword has no visible effect.
However, if a high-level spellcaster used Greater Magic Weapon on your sword they could make it a +5 keen longsword for the duration of the spell.
Sorry for the long answer but your post contains an incorrect assumption.

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No.
It only works on non-magical weapons.
I hate to be a pedant but I don't want to give a new player an incorrect understanding.
The spell does work, its enchantment is laid upon your sword. However, it does not have any useful effect because it is using the same type of bonus that is already on the sword.
This is important for the clear understanding of other spells (Greater Magic Weapon) and recognising that the spell will still work upon unusual magical weapons which have no enhancement bonus (for instance, if somebody cast a permanent light spell on a normal sword).

Korwynne |
Slightly off this topic, what happens when you cast magic weapon on a basic longbow?
If facing off with a creature where only magical weapons do damage, does the bow then infuse the arrows with magic, or does magic weapon only add +1 to hit, while the arrows are plain arrows doing nonmagical damage?