I overline my small stream rod. Sometimes By 2 1/2 line weights! I do not generally overline my larger stream rods.
The reality is that it depends largely on the distance you want to cast. With any given rod, if you are going to ONLY cast very short distances, you are probably better off overlining it. If you are ONLY going to bomb out casts, you should probably underline it (if you are casting far and want the heavier lines for wind concerns, start with a higher weight rod!). At average distances, or varied distances (most leeway), stick with the rod's natural rating (which may be different than the labeled rating, depending on model).
Fun, isn't it. Yeah, we're coming full circle. At the shop, they hand you a strung reel and a bunch of rods. You start bombing out casts, and buy the rod that'll throw a whole freakin line. You ignore the one that feels best at the distance you will fish it. And the rod which cast that whole line is the stiffest one, that should be rated higher. It casts so far because it's underlined. That's a 5 wt line they gave you, and that rod is actually a 6wt, despite being labeled a 5 wt.
Now you have your mislabeled 6 wt at home, and you bought a 5 wt line to match, and now you don't like how it feels when you actually fish it at normal distances. It's not loading. But you have this unnatural objection to overlining, a rod labeled a 5 wt just should not have a line labeled a 6 wt on it. So, somebody re-labels a 6wt line as a 5 wt for you. At some point, somehow or other you try out this line. And then you go online raving about how great this line is that turned your rod from a dud to a great fishing tool, buy the line, and every other idiot does the same and loves it too for the same reasons.
Today's 5 wt just became yesterday's 6 wt, both rod and line. Congrats. You've re-invented the standard.
Rinse and repeat. Soon, this rod and line will be labeled a 4 wt, and then a 3 wt, etc. And someone will wonder what this whole light rod/line craze is.