There are three types that have 7 weaknesses - the most of any combination:
Lunatone and Solrock are the only Psychic/Rock Pokemon but they also have Levitate which means they only have 6 weaknesses (and no double weakness).
Exeggcute, Exeggutor and Celebi are Psychic/Grass - weak to 7 types including 4x to Bug.
Snover and Abomasnow are Ice/Grass - weak to 7 types including 4x to Fire.
Those 5 are statistically the weakest Pokemon.