Most refuggios offer a cot or bed with a blanket and a pillow. While all the refuggios I stayed at were very clean, the blankets aren't washed after every use. I'm not sure if the pillows ever receive any care. So, being prepared with your own sleep sack or sleeping bag is essential on your Camino de Santiago. The goal is to keep it as light as possible while still being comfortable.
The most important factor when it comes to choosing a sleeping bag is the time of year you'll be walking your Camino. If it's late spring through early fall, a lightweight sleep sack will be plenty. If your walking fall through winter, you'll need a sleeping bag (and possibly a liner) that will keep you warm at night.
Next to your backpack, your sleep sack or sleeping bag will probably be the heaviest single item in your pack. So, it's worth shopping around to find something light and comfortable.
The lightweight sleep sacks provide coverage and comfort without being heavy or bulky. The sleep sack that's pictured above is just under 1.5 pounds.
It's also an option during the cooler walking months to carry a sleep sack and a liner. The liners can add 10-30 degrees of warmth without adding much weight to your backpack. (This one is only 11 ounces!). And, a liner like this can also give you some pillow hygiene.