Chadd says:

I’m by no means an expert on fly rod and line weights, but while outfitting for various outings, I’ve asked about this, too. My impression is that the fly fishing weight system is forgiving enough to easily allow one weight in either direction without significant detrimental effects to performance. In other words, if you have a 4 weight rod, you could go down to 3 weight line or up to 5.

I have a 4 weight rod that I "up line" with 5 weight line because it gives me more distance. I have also fished with mismatched rods and lines because of expedience and sometimes the mismatch is noticeable and sometimes it’s not noticeable at all. Why are you doing this? Is it an experiment of some sort or do you just have mismatched gear?

In any case, I’m fairly confident that you can fish with this combination of gear. Unless you’re some kind of supercaster with tiny performance tolerances (and if that was the case you wouldn’t be asking this question), you will be able to get a fly out there and catch fish. I think your reach will be fairly limited because the 3 weight line is so much lighter than the rod, but you can make do. Having said that, considering that this is a 4/5 weight rod, the difference between the upper recommended weight and the fly line is 2, not just 1. Kinda hard to say what will happen. Would I want to fish with this setup all the time? No.

Obviously, the best thing to do is string it up and go out on the lawn and find out.

The Wormist says:

l just want to give you a second vote of confidence on Chadd’s answer.
you can commonly go up/down one line weight with very little problem.
thumbs and BA, Chadd.