My washing machine will only spin if very light load, otherwise it tries to spin but just goes back & forth.?

The repairman thought it was due to clog in drain pipe. The pumber said it must be the washing machine. Snaked the drain and the problem still continues. Spinning 3 towels at a time is not for me. Like this low tech Kenmore and it has worked for 25 years. Hoping it's not time to buy new one but will if can't solve this problem. Next step is to get the Sears repairman out here. Any suggestions...other than "buy the new one"??