Additive secret sharing achieves perfect secrecy: even if a strict subset of shares is leaked, the secret remains completely hidden. But is this still the case when partial information on every share leaks?
We study the local leakage resilience of additive secret sharing (and its variants) against Hamming-weight leakage in two settings.

• Over binary extension fields (Boolean hypercubes), we show that inner-product secret sharing  (where the secret is reconstructed as an inner product of the shares with a fixed vector) is secure against Hamming-weight leakage unless the reconstruction vector is constant. We also introduce an efficiently computable score function that quantifies and certifies the security afforded by a given reconstruction vector.
• Over near-dyadic-order groups, we show that additive secret sharing is secure against Hamming-weight leakage. We prove matching upper and lower bounds on insecurity, establishing that our bounds are tight. As a byproduct, we obtain a ternary representation result: the Cayley graphs of near-central Hamming slices have diameter at most three.

Our analysis is Fourier-analytic, combining techniques from Krawtchouk polynomials, additive combinatorics, and spectral methods.