some things i dont understand about your list (and theory) is that, based on the list, what you said you make palkia practically equal to dialga. heres what i think.
Here are Palkia's weaknesses:
Normal - Half Damage
Fire - Normal Damage : something tells me you just copied the two lists, or just forgot to change this. water and dragon together and fire doing normal damage?
Water - Half Damage
Electric - Normal Damage : Palkias dragon part voids his water parts weakness to electricity
Grass - Normal Damage
Ice - Quarter Damage
Fight - 2x Super Effective : since when has dragon or water either been weak to fighting?
Poison - No Damage
Ground - 2x Super Effective : same thing as fighting, water and dragon arent weak to ground.
Flying - Half Damage
Psychic - Half Damage
Bug - Half Damage
Rock - Half Damage
Ghost - Half Damage
Dragon - Half Damage : Dragon is weak to dragon in case you forgot, and since water isnt, id say that palkia (and dialga) are weak to dragon.
Dark - Half Damage
Steel - Quarter Damage
although i prefer dialga in image and on my personal likings, i think palkia has a slight advantage with their given types.