I was going to quote and comment but that would even be more confusing I'm a tad bit confused as it is!
First let me state where I am coming from, the longer I fly fish, the more I appreciate a (1) light first and then a (2) balanced outfit. Balanced with the line weight and flies being cast. Balanced with the use whether it be Bonefishing or casting for Bluegills. Lastly I like it somewhat balanced in hand.
Try this on for size. If you do not let your rod do the work, most generally you'll find casting a tiresome chore and not be very good at it for certain as forcing the rod is a poor substitute for skill.
Not only does balance plays a part here, it's two fold in it's application, and we have (1) static and (2) dynamic balance that is of concern. Carry a tip heavy outfit from your car to the stream (realitively static) and you risk drooping that tip and snapping it off!
Cast an outfit where the reel/backing/line doesn't somewhat offset the length of that fulcrum and line paid out and again it's not pretty to watch and is tiring while becoming much more so with heavier and longer outfits. With todays rods and reel outfits being so light and lively we find much of the balance of which we speak is a given and built in.
Speaking of line speed during the cast and you'll find that if you get more than a line size or two off the recommended size your line speed goes haywire!
Line, line length out, the lines weight, the length of the rod and even the flex of the rod (that determines effective rod length when moving) all determines a good match when it comes to a dynamic balance.
When speaking of line speed
coupled with the line's weight we are speaking of momentum, not energy as it's simple momentum that will or will not carry line in the shoot phase of that cast and it's minute adjustments with your hand and wrist that keeps the entire casting plane where it should be. The minute that gets a bit out of kilter your casting distance suffers and accuracy suffers even more.
From above, "The longer the cast, the lighter the reel end of the rod becomes and the greater the variation of the force on the rod tip. I suppose that if you make very long casts on a routine basis, you might prefer a heavier reel to counter the forces on the rod tip... "
Good point and that's likely one of several reasons that the Charletons, Tibors, Abels and Pates and all their copies (all high capacity, heavier reels) are often the premier choice for salt water fly casting reels.
Although the rod and the reel are on the same side of the shoulder-elbow fulcrum when we cast an unbalanced outfit the applied torque on wrist and hand joints will try and bend the hand and wrist causing fatigue, accuracy and distance problems.
One thing is for sure that todays rods and reels are much lighter so we can go for an ultra light reel and it will balance the rod which are much lighter also. When fishing with most fresh water outfits the weight is so neglibible when compared to rods and reels of old that it's hard not to balance the outfit when it comes to reel weight/size compared to the rods.
On fly shop testing: yes a certain amount of testing a rod is done in shop with and without a line loaded reel preferrably.
If it balances about midway down the handle give or take an inch with the reel on, it should later feel good in hand when casting.
Being careful to not hit display cases, etc wiggle the tip and watch the rod. This tells you how responsive the rod is and how quick it returns to the null position once flexed and then relaxed.
It also begins to tell you whether the rod is fast, medium or slow. Place the rod tip on the carpet and holding the handle about waist high observe the flex obtained with just the rods weight minus the reel. Again this helps sort out the flex of the rod whether it be full flex, tip flex, etc and when done with another manufacturers rod beside it in a similar flex gives you some idea on which manufacturer has the fastest or slowest rod for a given stated line weight.
Lastly though you should try before you buy and at least lawn cast the rod, of not cast it on a practice pool whcih some shops have. Note the feel of the rod with the reel supplied and from that you'll perhaps decided you'd like a heavier but more often than not a lighter reel.