A picture of the bin would help but maybe you don't yet have a bin? How large a bin are you thinking about? What kind of worms? So many questions...

Besides squirrels I think you will have to guard against other rodents such as raccoons and you prob have ground moles also. Depending on what you plan to feed them the food may attract other critters.

So I think you would need some protection from the ground critters and as for the cover I would use hardware cloth for both. Are you building this or is someone else? And just what do you call heavy?

Would putting the cover on hinges help? Or something with those mini shocks like used on car hoods, trunks, etc. You can find something to place on the cover to keep out rain like a shower curtain or a plexi glass type material.

Or use a plastic bin with the bottom removed for drainage but replaced with hardware cloth to keep critters from tunneling in.

Hope that gives you some ideas if that is what you were looking for.

I can't do heavy lifting either, and bending, stooping and crouching are also an issue for me. For this reason I would find it difficult to tend worms in a pit in the ground. Are you able to buy, build or have built for you an outdoor bin at a height you can reach more easily? It doesn't need to be fancy. A lot of people use basically a wooden chest or a converted bathtub.

Here is a Youtube video from a gardener I'm a fan of, showing his outdoor worm bin (he also has indoor bins as part of his set-up)

https://www.youtube.com/watch?v=z6e5Hy-aIHc&index=10&list=PLApXYvbprElznAWWNqp-JxiAS4io8dQWh