...budget constraints do not permit proper framing?
How about improper framing?
I've been framing as a part time / home business for something like 10 years now, so find it hard to argue against the benefits and value of decent framing, but I fully understand that budgetary constraints are important. So, for what it's worth here's a small sample of my thoughts and opinions:
First and foremost: Protection. If you've gone to the trouble of making quality fibre prints, they deserve to be behind glass. Dust, dirt, airborne pollutants and grubby fingers will all affect the print and mount/mat at an alarming rate. Edge damage to the mount will also appear as if by magic.
Secondly: Flatness and rigidity. Quality mountboard is often manufactured to have a curvature which helps to keep the artwork nice and flat against the glass in a frame (ie. prevents bowing backwards out of the frame). The bigger the mount, the more pronounced the curvature, and with your print size of around 16x20 inches, I'd guess your overall display size is likely to be 20x24 inches. Without the rigidity of either being stuck to a stiff backing, or pressed firmly against glass, the curvature of the boards may detract from the visual impact of your display.
The curvature can be mitigated somewhat by reversing the backing to counteract the bow of the cut mount (assuming the "mount back" is the same type board as the cut mount - common practice), but that will necessitate fairly high-grab adhesives - again, if I'd made some nice fibre prints - I wouldn't want them in close proximity to lots of sticky stuff..!
Francois mentioned acrylic as a lightweight alternative to glass (styrene is even lighter and cheaper), but in my experience, 2mm float glass is cheaper and more rigid at this thickness (I buy 36x48 inch sheets at £5 + vat each - an equivalent sheet of [floppy] 1.2mm styrene is almost double that price).
If cheap ready-made frames from the likes of Ikea are still busting your budget, how about "clip frames"? They're cheap, reusable and universally available.
Or you could make up your own Passe-Partout. A simple sandwich of backing board, mounted print and glass, all held together with decorative taped edges... you could even use a tape to match your mount colour, giving a very minimalist look.
I hope some of this helps with your decision.
Please do let us know how you decide to go on, and show some pics of the display.
(edited to correct acrylic / styrene confusion - apologies)