Can I fly a UAS that weighs more than 55 pounds within my own private property if I stay below say, 200 feet? I do not have 333 exemption
According to the FAA Part 333 rules, all UA aircraft (> 55 lbs) must register with the FAA with an N-number before flight. As far as I can tell, the rules don't specify zones or altitudes where the regulations aren't in effect, so I think it is highly advisable to register.
My personal rationale
Being safe just in case is far better, at least in my mind, than choosing to avoid registration. I know people in my RC Quadcopter possee that fly sUAS aircraft but don't have Part 107 licenses. I have one, (I would rather be safe than sorry) but I could see how as long as you are careful, flying a small sUAS without a Part 107 license isn't such a terrible option.
In my mind, UA aircraft are an entirely different story, as they are inherently significantly larger than sUAS aircraft, and if something does go wrong, damages would be more severe. The risks (not to mention the responsibility) involved are far more substantial, and I would never consider flying a UA aircraft without a license even if I was only flying on my own property.
Flying over your own property doesn't matter. As soon as you leave the blade of grass, whether at 1 inch or 1 mile, you are under FAA domain.
Therefore in your case, you would need to comply with appropriate regulations.
If you have a special application, or you are doing some specialized development, you might look in to a waiver. But in general, expect that all the rules apply to you even if you are over your property. This includes prohibitions about flying over people, night operations, etc.