Bulky and heavy? The stock rifle weighs 5 lbs. Adding a little meat to it isn't going to drastically make the gun "not fun", or uncomfortably cumbersome. Especially if the rifle has a strict range and gun safe life. If you truly want to know heavy, carry around a M240B for a bit, deff not fun.
Not to mention, if you purchase a centerfire AR the 3x and red dot will easily hold up to the increased recoil and stress. I've seen soldiers have both sights on their weapons with no known complaints or problems. Besides making it to easy to get an Eagle Eye on a qualification.
Here is my rifle. Please ignore the fact that my camera is made by Fisher Price and my skills are equal to that of a emu with downs.