Thanks for a very intriguing question.
The phenomenon you are referring to -- where the males and females of
a species are dramatically different in appearance -- is known in
biological circles as sexual dimorphism. A Google search on [
"extreme sexual dimorphism" size ] led to an article on an odd
creature called the blanket octopus, which seems to be the animal
you're looking for.
First encounter with a live male blanket octopus:
the worlds most sexually size-dimorphic large animal
"Our observation...of a living male...off the northern
Great Barrier Reef, Australia... The animal approached dive lights at
c. 8 m deep. It is 2.4 cm [note: one inch] in total length and weighs
0.25 g. It is mature with a fully developed testis and reproductive
By contrast, females...attain sizes of up to 2 m long (Nesis 1987)."
So there you have it -- a one inch male and a 2 meter female.
I had actually expected the answer to be the anglerfish, an oddball
staple of public television nature documentaries. The male of some
anglerfish species is not only tiny, but a parasite to boot:
"...nowhere is mating more bizarre than in the case of some deep water
anglerfish. The tiny male, only about one and a half inches long,
latches on to the much larger female which can be up to 45 inches
long, and over time his body becomes a fixed appendage of hers, a mere
sperm producing organ of the female."
So this creature, too, almost -- but not quite -- meets your size
criteria. And I can't resist closing with this quote from a one Dr.
Caruso, one of the world's leading authorities on anglerfish:
"The male is parasitic, and essentially nothing more than a
self-propelled pair of gonads directed by a nose."
Whew...makes me glad to belong to good old homo sapiens.
I hope this is the information you need. I strive to give the best
possible, but if you feel additional information is needed, please
post a "Request for Clarification" before rating this answer.