There are plenty of inexpensive ebikes thses days, but they're not light. Think around 50 pounds.

I've converted a number of existing bikes to electric. A small 250W-350W motor is under 5 pounds. A small battery is about 4 pounds. Electrics add 2 pounds. If you start with a light bike, you can finish with an additional 11 pounds. For cost, you will pay about $600 for the drive train, although some of us can get by with lower cost batteries. That's about where inexpensive ebikes ate in price.

My lightest full size bike is a 700cc Diamondback Mara Vista. It's about 45 pounds with a 250W 36V rear motor. I have some 20" folders that are 36-38 pounds and a 20" mini vello that's maybe 33 pounds. Might get another one.