SYDNEY - Asian share markets were mostly weaker while the U.S. dollar higher on Tuesday as investors awaited inflation readings from China and the United States to deliver an updated outlook on the health of the global economy. MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.9 percent on Tuesday, after U.S. stocks ended the previous session with mild gains. The index is down 2.8 percent so far this month. The yield on benchmark 10-year Treasury notes rose to 4.0885 percent compared with its U.S. close of 4.078 percent on Monday. The two-year yield, which rises with traders' expectations of higher Federal Reserve fund rates, touched 4.7682 percent compared wi...Keep on reading: Asian markets softer as investors look to key inflation readings