Much depends on when you plan to walk, and how much you are prepared to risk being cold.
I walked the
Camino Frances in late Mar, and arrived in Santiago in early May, and carried a +5dec C bag and 'silk' liner. All up in a stuff sack, about 1.1 kg. I would not have been comfortable in several place at that time of year without it. In contrast, I knew of people who were walking with a thick liner, and at least one of them suffered badly on at least a couple of occasions when either there weren't blankets, or weren't enough.
If your sleeping bag weighs a couple of kgs, its probably too heavy for the circumstances. My other bag is 1.8kg in a sack, and it is rated to -5 dec C. In cold countries, it would count as a three season bag, here in Australia it covers four seasons where I live. At the time that I walked, there was never anywhere you would have had to sleep in the open, and need a warmer bag than around +5 deg C.
I saw blankets in most albergues, but I cannot recall whether all of them did.
As a minimum, you should carry a liner, even if it is only a lightweight one. Only once I got further into Galicia did some of the albergues provide disposable sheets, and there were only a couple that did that.
Regards,