Since you didn't say, let's assume you're dealing with stock components, and an unrebuilt (original) engine with xxxxxx miles on it...
The FSM lists your springs as 80-90 lbs. at a 1-11/16" installed height.
If yours are loose enough to spin by hand, you obviously don't have 80-90 lbs. pressure on them.
This could be due to several things:
1.) Soft springs. They're 53 years old.
2.) Sunken valves. As the valves/seats wear, the valve sinks deeper into the head, increasing the installed height of the springs and reducing their seat pressure.
3.) During a previous rebuild, the spring seats may have been cut/deepened to accommodate non-stock springs and/or valves, so now the stock-type valve springs are too loose.
4.) The valve seats were over- ground during a previous rebuild, again sinking the valves too deep into their seats.
So, what to do? Put a straightedge across the valve tips- you'll have to remove the rockers to do this. With the straightedge in place, are all the valve tips even? If some are noticeably higher than others, you probably have sunken valves- time to have the heads rebuilt.
If they're all even, you could still have sunken valves, so it's time to measure the installed height. If it's over 1-11/16", You may be able to get away with installing the correct thickness shims under the springs to achieve your correct installed height, and thereby regain your spring pressure. This, however, does not address the reason your valves are sunken to begin with (probably bad or overcut seats).
If your installed height is correct and there is still insufficient pressure in your springs, then the springs have gone soft. Time for new springs.
My guess is that you'll have to pull the heads and have them gone through.
Edit: First I would shim the springs if needed (if the valve stems are all even), then run a wet compression test to determine the condition of the seats.
