I have the factory engine weights, they are sitting on a shelf.
I removed them because I found it made my attachments ride/bounce up too much, especially my snow blower. With the flail mower I don't miss the easier lift when turning -- I take a curve instead of turning in place.
Even without the engine weights, I've considered adding weight to the flail mower to keep it from bouncing upwards when mowing uphill or on very rough ground. Very little of the area I mow with it is flat, so about half of my strips are uphill.
The only attachment where I miss the engine weights is the generator. This would probably be different if I had any soil-working attachments which tend to be heavier where you want to turn on a point.
As for the handles, I haven't bent or broken them yet. I did, however, snap the pin in the height selector trying to muscle my snowblower out of a hole when the engine was already lowered onto hard packed snow. I count that in the abuse category though, I was half hanging off the handles.