I don’t have any specific recommendations, though I have tried a few of Sony’s newest primes and a couple of GM zooms—on an AIV—and been impressed by all of them. But I have a general point:
It’s not the weight (or the size—unless you’re one of those photographers in the US who seems to be afraid that anything bigger than a pancake lens on a small body or a Ricoh GR is an irresistible invitation to a mugging*) of the lens that matters most, although many commenters seem to think so.
It’s how it balances on the camera. I’ve always found that far more important over forty-plus years of a variety of SLRs and their successors. Unfortunately, that’s really a matter of experiencing it for oneself, so I’d suggest either finding a Sony ‘try before you buy’ show, or hiring the most likely candidates for a couple of days: especially if your chosen few comprises the more expensive GM’s!
In my, admittedly limited experience, Sony’s ‘Mkii’ and newer GM lenses generally seem to be both lighter (an advantage for carrying a collection around as much as use on-camera) and balance very well on the smaller and lighter bodies, with good access to the lens controls as well. Also important. But they are rather pricey.
(In choosing, I’d also be cautious about any reviews that suggest older lenses might not resolve well enough for a high-res sensor. Mostly, that seems to be opinion rather than scientifically—or even observationally—proven.)
NB: The only small Sony’s I use are actually an NEX-6 or an A6000, but some FF lenses, and even some A mount teles with an adapter, don’t cause any handling problems with either. A big tele on a tiny body does look a bit odd, but do we really care?
* I doubt if however small a camera plus lens is, once it’s out in the open, if a thief wants to, or can, grab it, they will. Considerations of size (or ‘pocketableness’) never stopped thieves stealing iPhones.