I would not repair a machine like that; not worth the money. I would also never buy a non-vintage Singer.
Walmart has some nice Brother machines that are light in weight and relatively inexpensive. One good thing about buying a machine there is that you can try it out and make sure you like it; as long as you have the receipt and are within time (30 days? not sure), they are good about taking machine returns.
A lot of people like the Janome Jem, which weighs about the same as a Singer featherweight. There are different machines within that line, depending mostly on number of decorative stitches. There are other lightweight Janome machines that are inexpensive also. Check Amazon for "janome jem" to see the possibilities. Weight is always listed in the specs on Amazon; as long as you keep it around 12 lbs it will be similar to a featherweight. You can also read all the user comments about specific machines to get a better idea of what they are like. Amazon is very good about returns too, as long as you are within the time period. If you simply don't like the machine, you need to pay return shipping; otherwise return shipping is free if there is something wrong with the machine.
Overstock sometimes has refurbished Janomes and Brothers too.