I also think it's turntable dependent. However I think it best to "follow the physics" so to speak.
First let's assume a concrete slab-on-grade floor with a rigid rack or stand, or alternatively, a wall-shelf lag-bolted into a brick/block wall. So much for floor/shelf-borne vibes. I mention this because those mechanical vibes are most always of much larger magnitude than airborne vibes -- and if one is trying to hear differences in dustcover configuration, will muddy those waters. And while we're at it, let's assume zero vibes from the TT itself; except for the stylus wiggling in the groove.
The second thing to consider is the path the vibrational energy has to take, getting from the air to the platter (without any dustcover in the way, for now) where presumably it will muck up your music by causing the platter to vibrate or even resonate.
Now I'm not of the 30kg. platter school but with no dust cover, or an open dustcover, heavier is definitely better, simply because of a large amount of resting inertia - especially true if the chassis is sprung. So far so good?
NOPE! Unless your TT is RIGHT in front of the speaker, and the bottom of the platter is somehow sealed off from the room air (not!) the air pressure will be equal on all sides of the platter, with the pressure wave striking it essentially equally from all sides. So, with the DC up or off (doesn't matter which) the air vibrations will not move the platter (suspended or not) because they impinge on it equally everywhere. BTW, if the DC is up (like a sail?) not a problem. Again, it is struck by sound pressure waves equally on both sides. And one other thing, because most dustcovers have a diagonal dimension of roughly 2 feet, they would only "see" frequencies above approximately 300Hz. Everything lower would flow past them with no effect ;-)
In almost all cases where someone detects their TT 'dancing to the music', the vibration is getting to the table thru the floor or (less often) the wall to which the shelf is bolted.
DC down could be a possible problem IF:
1. The edges of the dustcover fit tightly to the plinth all around. And,
2. There is no opening through the bottom of the plinth to allow easy equalization of the air pressure between the top and bottom of the dust cover. And,
3. The DC is made of unbelievably thin plastic ;-)
Other than that, I don't think it matters - except for one thing: it is a DUSTcover after all! And no matter how clean my records, or my air, if I leave it up during play, some damn piece of crap ALWAYS SEEMS TO LAND ON MY RECORD!
So I close it ;-)
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