By Scott Murdoch SYDNEY (Reuters) – Stocks and oil weakened on Monday as rare protests in major Chinese cities against the country’s strict zero-COVID policy raised worries about management of the virus in the world’s second-largest economy. MSCI’s broadest index of Asia-Pacific shares outside Japan was down 0.6%, after U.S. stocks ended the previous session with mild losses. Australian shares lost 0.47% while Japan’s Nikkei stock index was down 0.37%. South Korea’s KOSPI 200 index retreated 1.35% in early trade and New Zealand’s S&P/NZX50 Index was off 0.4%. In China, demonstrators and police…