Brother makes a mechanical machine that is reasonably light weight for under $80. I have two - one for traveling and one for in my garage, where my LA is. I don't know if you have a 'wheelie' bag for your current machine, but you can get one of them very reasonably for about $50. The bag makes transport of any sewing machine much easier. If there is someone at home who can put the wheelie in your car, there is probably someone at your church group who would help you get it in and out at that end.
You could also use a carry-on bag with wheels to transport a machine.
Janome also makes a small machine, 5 pounds, that is easy to transport. I have one, but seldom use it because the one I have does not allow me to change the foot. However, I purchased it about 6 years ago, so maybe that feature has been changed. Other than that, it is a great little machine.
https://www.target.com/p/janome-comp...B&gclsrc=aw.ds