Strength is barly needed anymore. Machines do most of the work, and some frail people are the most intelligent... Like me. And besides that, all the weak people whould team up, and as long as there strong enough to hold a gun, your in trouble.
First off, regardless of how it happened: Just because the word "weak" was used, that does not mean physically. Weak in this context refers to mentally feeble, prone to illness, etc.. Physically weak/malformed also can apply here, just not only.
Keeping that in mind, I ascribe to the idea in a form.
Not so much as "Kill 'em all", yet more of a "If they fail to survive, oh well."
[Physically weak/malformed also can apply here] Stephen Hawking is deformed, but he is quite useful (at least for science) Indifference to the weak is morally wrong; Caring for those who are weaker than us is indeed what separates us from animals, or people like Hitler who are scarcely any better.
Kill the weak has nothing to do with social Darwinism. Social Darwinism would simply allow those not strong enough to survive to perish due to their own weakness. There would be no need to kill the weak as they would die due to their weakness.