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It doesn't qualify for Weapon Finesse, as it's not a light weapon...

I asked because short sword is light weapon and it's bigger than dagger [and it can be used with finesse], so I presumed that a medium sized dagger would be something similar to short sword for small character. Or not?

Edit: But it's not well balanced so it probably couldn't be used with finesse.

A small sized PC, using a Medium sized light simple weapon, in this case a a dagger (assuming he/she is proficient in such weapon) would incur a -2 attack penalty for size difference, correct?

Do I still get the Weapon Finesse in that case and does it still count as dagger proficiency wise?