I think what you really want is a string trimmer.
String Trimmers - Trimmers & Edgers -*The Home Depot
A piece of plastic 'string' spins around horizontal to the ground and cuts what it can. You just run the business end of the trimmer along the ground and it whacks through weeds. You have to continually feed more string out from the spool because it breaks off frequently. Some do have a plastic blade which is tougher, Weed Eater is just a brand name. The weeds don't get eaten.
An edger is different, it has a wheel or blade that makes a vertical cut along the edge of concrete or brick. you can use a String trimmer for this purpose if you hold it at the proper angle.
My lot is about .3 acres and I have an electric trimmer. I prefer the electrical cord to dealing with gas.
a mower just cant get into those crevices the same way as a trimmer.