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7 weaknessesGRASS / ICE (3)GRASS / PSYCHIC (4)GRASS / DARK (4)FIGHTING / ROCK (1)PSYCHIC / ROCK (2)ROCK / DARK (2)
Dual type chartin this site mentions 6 dual types having 7 weaknesses, i.e. the most no. of weaknesses.
Grass & Ice:AbomasnowlineGrass & Psychic:Exeggutorline,CelebiandCalyrexGrass & Dark:Shiftryline (not Seedot),CacturneandZarudeRock & Fighting:TerrakionRock & Psychic:Lunatone and Solrock have Levitate, so no Ground Weakness. They are ruled out.Rock & Dark:Tyranitarand its Mega.
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,ExeggutorandCelebiare Psychic/Grass - weak to 7 types including 4x to Bug.SnoverandAbomasnoware Ice/Grass - weak to 7 types including 4x to Fire.
Those 5 are statistically the weakest Pokemon.