Could you do a trial by piling on blanket/linens/towels/clothes/pillows on top of your regular blanket(s) at night to add weight, and seeing how it feels with the extra weight? (Or by finding some other way to add temporary weight to your blanket(s)?)
It could be a challenge to get it all balanced and not have it be lumpy and to keep it from falling apart (if you move around a lot in your sleep and don't have enough blankets/sheets to just pile them all up to a good enough weight)...but, if it didn't interfere with your comfort, one idea for keeping it all together and evenly balanced would be to use safety pins to keep everything in place.
Another idea would be to use a sleeping bag (or two of them zipped together, if you have access to 2 sleeping bags without having to buy them..... to make it normal-blanket-width but still a sleeping bag) and then put whatever you're using for extra weight inside the sleeping bag(s)....stuff might still shift around if you move a lot in your sleep, but to a lesser degree.