Up close, casts within 20 feet, casts for normal small-stream fishing, a decent rod will cast about any line. I'd be willing to bet my favorite small-stream stick, a Diamondback 7ft 4wt, would cast a 10wt line, or a 0 wt line. But, that doesnt mean it will feel good in casting, or land delicately as not to spook fish, or be comfortable. If you come to a place where you need to cast further, having the wrong line on the rod will be magnified a ton. I've never cast a rod at all distances that done so equally well jumping 2 line weights, up or down. I'd hate to come to a pool where I really needed to stretch a cast 30 ft or so and have my rod just bottom-out on me to the point I couldnt cast accurately at the distance needed. Most major rod manufacturers have spent alot of time, research and money into their line of blanks, and if they mark a rod a particular weight, then I've found it to be mighty close usually. For me, a rod needs to perform with the line weight chosen for it at most normal casting/fishing distances. Jumping 2 line weights up or down has never worked out very well, for me anyhow.
If your rod manufacturer says the rod fits a 4wt line best, thats definitely where I'd start and if it just doesnt suit you, then try uplining one weight. If that still aint enough, then I'd try another rod with a different action. Some folks just dont get along well with a fast rod and/or a slow rod. It's a matter of personal preference of rod actions and casting styles most of the time and not necessarily a line weight problem.
Hope this helps some, and tight lines to you!