Are you using any case or stand?
It definitely is heavier, and its size does mean I have to think a second before picking it up. If I grab it by a corner, that would definitely cause a "oops" moment as the weight would twist it against my hand. I have to take care to pick it up by the middle of an edge. The Air is so light I can pick it up any which way without thinking about it. I also decided to just go with a TPU back case, and forego the Smart Cover, because I feared the combined weight of back case + Smart Cover would make the iPP too heavy. There are definitely moments when I glance at the iPad Air, thinking longingly of it's almost weightless ease of handling, then I look at the gorgeous 12.9 screen, and I never pick up my Air after all. But I can definitely understand how some people might prefer the 9.7 form factor.
Oh it's definitely noticeably heavier than my old Air 2, but no, definitely no case in normal use, it makes it far too heavy.
I do have the Smart Keyboard but that's fine as when I'm holding the Pro I just detach the keyboard. I've also got a nice leather case for it just in case I'm going anywhere that's going to demand a bit of extra protection in transit. But again it'll be coming out of that most of the time to use it.
I've got a skin on the back to protect from scratches and other than keyboard use, that's all I have on it when I'm using it. Which is great, I always fit skins because they basically add no weight or bulk.
I can't hold it by its edge with one hand for long because of the nerve damage, so I've taken to putting my hand across to the opposit edge of the iPad and letting it rest on my forearm instead of holding it at the edge (kind of like the way you'd hold a clipboard.)
I find it extremely comfortable and well balanced that way and it doesn't aggravate my injury which is a major aspect. If it caused a problem I'd have to get rid of it no matter how much I like it.
But yeah, screen size/weight and, well, all aspects I suppose are very personal things, none of us are exactly the same, thank god
My wife point blank refuses to own an iPad bigger than her Mini 4. I was tempted to buy her an Air 2 instead of the Mini 4 at the time (it was a surprise Christmas present, or birthday I forget which, she got the Waych for one, iPad for the other) but in the end I knew she'd have clubbed me over the skull with it because it would have been too big for her. She is only a dainty wee thing.
*Edit
Ooft, sorry, kind of rambled off on one there. I've had to take extra meds today so I'm high as a really high kite, makes me waffle