Another fairly light weight machine is one of those little Kenmore machines - I forget the number - they look like they are in a hair dryer case with flowers embossed in the sides. They go for $50 - $100 around here - well if you can find one. They do zig zag and a hem stitch and one or two more besides straight stitch. They are a well made little machine.
Some people like the Singer Genie and other old mechanical zz machines. They are light weight but do have stamped metal parts - the tension is tricky to figure out. Elna is a good machine and there are some older models that are light weight. I'm thinking the European machines that are small and light weight are good - remember if someone says it is a good machine doesn't mean you shouldn't test the machine out yourself when you buy it. Look it over good - is it clean? Test sew. You see a lot that way. Take some time - you see a lot that way, too. I have been fooled a time or two. I've gotten 'good' machines home and on the bench only to find they had problems. Again, look them over well.