TOKYO—A weak yen may be hurting Japanese households more than in the past, as the country’s increasing reliance on more expensive raw material imports pushes up the cost of living, Bank of Japan (BOJ) Governor Haruhiko Kuroda said on Thursday. Kuroda’s remarks are the most direct acknowledgment to date of the potential disadvantages of a weak currency, highlighting a growing concern among policymakers of the hit to Japan’s fragile recovery from a steady rise in input costs. “The yen’s depreciation might have an increasing negative impact on household income through price rises,” Kuroda told a gathering of business leaders at a conference in Tokyo. He repeated his view that overall, the benefits of a weak yen outweigh the drawbacks—yen declines make Japanese goods more competitive overseas, and boost yen-based profits that companies earn overseas. Still, he said, a weak yen can hurt households and domestic retailers by pushing up import …