My Kenmore front loading washer, model 417.43042200, won't agitate or spin to complete the cycle if the load is too heavy, such as 5 bath towels. If I take off the back and help turn the drum in the agitate or spin mode it will agitate/spin and complete the cycle. The pump still drains the tub. If the load is lighter, such as 4 dress shirts, it will go through the complete cycle without assistance. My wife feels that the clothes, however, are not as wrung dry as when we first bought the washer.
What might be the problem or problems?

Might need a new belt or motor could be tired.

The bearings in your tub/ drum assembly are most likely failing. Sometimes, as it is in my case, the basket & support spider can also break as well. Both of these problems are evidently very common on this particular washer model made by Frigidaire(Electrolux) and sold under many different names. These problems tend to surface after 4 years of age. I will post some pics on my own question/ post.