The Indian Rupee weakened by 35 paise to 45 rupees 29 paise a dollar in early trade at the Interbank Foreign Exchange today. This follows dollar's gains against other currencies.Besides, demand for the American currency from importers also kept pressure on the Indian rupee, according to Forex dealers. The rupee had ended 20 paise higher at 44 rupees 95 paise in the previous session.