I have been having this issue for a while and today, just for troubleshooting purpouse, I removed all GSX profiles and the problem disappeared. tested at Inibuilds EGLL and Aerosoft EDDM. Put again the profiles in the GSX folder and the problem reappeared. What is the reason of this I don't know, but if this may help I am glad to share my feedback.
Do these profiles add lots of VGDS? That's the only thing that, just because a profile loads, could affect performances, because by default, all VGDS are created as static objects, then the one for your parking will get activated when you activate the parking in GSX.
While the static version is highly optimized, with a fairly low visible range, so it should affect fps too much, IT IS an extra Simobject, and we know the total number of Simobjects in the sim can affect Simconnect adversely, and GSX depends completely by Simconnect being responsive so, even if the number might not be high enough to trigger disappearances or generic Simconnect/Navdata errors, it might be enough to cause stuttering, especially on such large airports.
Which is why, a while ago, we added an option in the DETAILS page of the profile, where you can Disable the creation of the static VGDS so, only the one in the active parking will be added, instead of possibly many dozens.
You can try placing the profiles back, but set the option to Disable the static VGDS, restart Couatl there, and see if you see any benefit.
Another thing in the profile that might affect performance, are long passenger walking paths because, the longer the path, the more passengers will be created at once, since they are removed only when the path ends. But of course, this would only be an issues if you ARE on these WALK-IN parking position. Unlike VGDS, which are created when entering the airport (unless you disable them), walk-in paths won't affect performance if you are not in one of those gates and call passengers.