Drafting film glued on plywood
Polystyrene sheets (thermocol is one brand) and cardboard sheets are your friends here! Take the polystyrene sheet, cut it one inch longer than the drafting film on all sides, cover the poly-sheet with colored paper or paint it (optional, and not really necessary as yours is oil painting, but would be needed if it's just a pencil or charcoal sketch), stick the film on the poly-sheet (don't use hot glue or superglue on polystyrene ever; I learned this the hard way), then turn the painting upside down, with the painting facing the floor poly-sheet on top, and stick a cardboard sheet cut exact to size and then long strips of cardboard for the sides and the extra inch you left earlier on the top.

Pros: Looks like a legit frame because of the brown color of cardboard, is much lighter, is very cheap and easy to get your hands on

Cons: Absolutely none

P.S. For the glass thing you were talking, you surely can put glass on it but that would make it sensitive and fragile, so maybe you can also try saran wrap or maybe OHP sheets. With glass you always have to be super conscious while handling it, and also while picking up from the sides so you don't cut yourself; this way it's just more kid/teen/student friendly. But if you're an adult and it's going to stay in your office or on a private showcase, etc, go ahead, use all the glass you want.