When bodies are thrown upwards vertically, the equations of motion applicable are
v = u + at
v² - u² = - 2 g s or v² - u² = 2 g s
s or h = u t + 1/2 g t² or s or h = ut - 1/2 g t²
The quantities v, g, t, s do not depend on mass.
Height reached when v = 0, so height = u/√(2g)
The Earth attracts all objects with the same acceleration due to gravity g. it is g which is responsible for increase of decrease of velocity. The velocity determines the height.
More mass or more inertia requires more force to make the object move with the same speed. So small object requires small force to move at speed, Big object requires larger force to throw, if you give it same initial speed. Muscles give more pain. Because you give more force. But as Force = mass * acceleration, the acceleration is same.