As air-breathing mammals, whales must once have lived on land and needed hind limbs capable of supporting the mammals’ weight.
Conclusion (in question stem)
The fragile hind limbs are remnants of limbs that land-dwelling whales once had.
Evidence
Whales are air-breathing mammals, which suggests they must have once lived on land and needed hind limbs that could support their weight.
Whales have the bare remnants of a pelvis.
The fossilized whale skeleton has fragile hind limbs that couldn't support the animal's weight on land and had a partial pelvis.
Evaluate
The background is essentially telling us that whales, the modern day version that live in oceans, evolved from a whale ancestor that walked on land with a full pelvis and limbs that could support their blubbery weight.
Currently, whales have no limbs (common sense) and barely have a pelvis.
It sounds like what we're looking at here would be some evolutionary middle ground between those two stages. As the whale transitioned from being land dwelling to being ocean dwelling, we'd see it go from full pelvis to partial pelvis to bare remnants of a pelvis. And we'd see it go from sturdy limbs to weak limbs to no limbs.
Goal
We are looking for evidence that makes it more plausible that these fragile hind limbs are indeed remnants from a time when whales were land-dwelling mammals.