Actually it's not a 6x weakness. Paras & Parasect are 4x weak to Fire. With Dry Skin this increases by 25% which makes it a 5x weakness (4x1.25). In bright sunlight, Fire does 50% more damage, which makes it effectively 5x1.5 = 7.5x normal damage.
And yes, those are the only two Pokemon that will take that much damage from a standard move without other boosts (although I would consider the weather condition the same type of boost as increasing Attack from Swords Dance).
Incidentally, Thick Fat ability does allow Walrein to take 1/8 normal damage from Ice (the lowest without being 0).