The simplest answer is: no, an object's weight usually will not change its falling speed. For example, you can test this by dropping a bowling ball and a basketball from the same height at the same time--they should fall at the same speed and land at the same time.
Does weight make you fall faster?
Answer 2: No, heavier objects fall as fast (or slow) as lighter objects, if we ignore the air friction. The air friction can make a difference, but in a rather complicated way. The gravitational acceleration for all objects is the same.
Does Weight Affect rate of fall?
Acceleration of Falling Objects
Heavier things have a greater gravitational force AND heavier things have a lower acceleration. It turns out that these two effects exactly cancel to make falling objects have the same acceleration regardless of mass.