Any suggestions on fixing this? I cut the mortise about 1/16" too large in both dimensions. :(
Enlarge the tenon
Oh I wish I could leave it at just that one sentence ^_^ But it's not obvious how you'd do that.
Usually the error in an undersized tenon is quite small and you'd glue slips of veneer to each side that needs it (often it's the cheeks only that need attention). Here you'll need to use thin slips of wood that you cut yourself. When doing this ideally you're supposed to match the grain orientation of the tenon closely but it's not that vital at this scale unless you were using a completely different wood.
Glue the packing pieces to the tenon firmly and wait for the glue to harden, then check fit and adjust if necessary, then glue the M&T as normal.
Loose fit? No problem, glue with thickened epoxy
This sounds sketchy but actually it's a perfectly reasonable way to go. Epoxy is one of the few adhesives that can bridge gaps while still producing a strong joint and if you thicken the epoxy with a fine powder (wood dust is usually used but there are other options) you can get it to a consistency where it stays where you apply it and doesn't slump from the pull of gravity.
The usual aim point given for the consistency you'll need here is similar to peanut butter1..... and if you use wood dust as the filler the mixture often looks disturbingly close to peanut butter!
For next time the obvious reminder is to mark out more carefully but you may have had the problem where your marking out was on the money but the walls of the tenon moved back unintentionally as you cut due to how you're chiselling, which is a common enough error when starting out2.
Now the best thing is to try to avoid this as you work, by working more carefully and stopping to check your dimensions every now and then, but there's a good workaround and that is cut your mortises first and then size the tenon to match. This way you'll never end up with an undersized tenon again. And usually it's much easier to cut a tenon to match a mortise than to cut a mortise to match a tenon anyway.
1 What has peanut butter got to do with epoxy resin? on Epoxycraft.
2 Normally when a mortise is sized to the width of a chisel you only really need to worry about the two ends, not all four sides as here.