When a character makes a physical attack, the character uses up some stamina, based on the item's weight. For example, attacking with the Giant's Sword costs 34 stamina per swing, which is a lot. If you are planning on giving a character the Giant's Sword (or any other heavy weapon), keep this in mind. It helps if you raise the character's stamina affecting stats (STR, PIE, VIT).

Of note, since the stamina consumption is per attack, a heavy weapon that gives extra attacks will drain stamina really quickly when used. The Tripleshot Crossbow is the best example of this; if you use it, you will quickly run out of stamina.

Stamina also matters for spell casters. The stamina cost of a conventionally cast spell during battle seems to be (SL + PL) * 2, so a level 7 spell cast at PL 7 costs 28 stamina. As a result, you may find your Elven Bishop to be falling unconscious frequently late in the game, so be careful of that. (It helps to have spells that restore stamina, of course.)

A few actions consume large amount of stamina. Breath attacks (including those used by enemies!), Turn Undead, Pray for a Miracle, and the use of instruments and gadgets tend to drain a lot of stamina. In fact, you should expect bards and gadgeteers to be running out of stamina frequently, and raising stats just to boost stamina isn't a bad idea.

Of course all this gets worse with increasing encumbrance. I THINK "blue" encumbrance does nothing, but once it's green it really starts to kick in.

Heavier weapons tend to have negative initiative modifiers, too. While that does help decrease their overall stamina usage, (due to having fewer attacks) it also tends to make them not worth using at the same time, since they'll still be doing less overall damage for more overall stamina used.

Honestly I've never actually found the Giant's Sword to be that useful. It just doesn't do enough damage or have useful enough effects to be worth the weight. Especially when you consider that the first one you can reasonably acquire is from the Mountain Wilderness, which also contains you such gems as the Dread Spear or Staff of Doom, both of which do the job of two-handed extended weapon better than it does.

I'm actually having my Ranger use a Giant's Sword in this playthrough. It does a lot of damage, and she can attack twice per round with it. It also helps that it has a 30% K.O. chance. Combine this with my Valkyrie wielding a Stun Rod and enemies are often disabled, allowing them to die rather quickly.

One advantage of these heavy weapons is that the only thing you *really* need is high Strength. The combination of 125 Strength (100 + 20 from Ankhs + 5 from Giant's Sword) leads to large amounts of damage inflicted on the enemy. The other combat styles don't benefit as much: One handed melee weapons do less damage than good two handed weapons (though Fang, Diamond Eyes and The Mauler are good reliably obtainable weapons of this type), shields are not needed for fighter-types because they get plenty of AC, and dual wielding gives you only half the strength bonus from the off hand.

By the way, there is another reason to raise Strength on a ranger: The Strong Bow, a powerful buyable bow that isn't too expensive, requires 85 Strength to equip. (Don't know what happens if you try to use a temporary boost, like from Superman, to equip it. Has anybody tested this?)

Well, I've just once examined the stamina consumption of different instruments on gagdets in terms of their required music/engineering skill, and this consumption does increase with increasing encumbrance.

Testing encumbrance's effects on magic stamina cunsumption:

In the yellow, PL7 Heal wounds costs 16 stamina

In the red, it costs 24. (Note that I tested this by having my Faerie Alchemist with low Strength hold the Giant Silver Nugget, so the cost likely doesn't get any worse than this.)

In the white, it costs only 8.

Anyway...

Out of curiosity, does anyone choose to wear lighter armor on their Fighters, Valkyries, and Lords because of weight issues? Does that approach work well?

Edit: More additions:

Green, cost 12.
Blue, cost 10. (This was a pain to test, because I had to drop nearly everything of significant weight. White was easier because Superman.)

I am actually thinking of restarting the game, but with the following differences:
1. New rule: No Infinity Helms. (With this rule, are Robes of Rejuvenation worth it for front line characters?)
2. Party has one change: Replace the Faerie Alchemist with a Dwarven Priest. This will give the party more carrying capacity, and has some other implications, both good and bad. Will focus on STR and PIE first with this character. (Which of DEX, SPD, and SEN is the best choice here?)
3. Setup differences: I think I'll still go Stun Rod with the Valkyrie. Ranger, I'm thinking, will go Mace/Wand dual wield this time. Bard will go Bloodlust until Fang. (This way, that weapon sees some use.) Gadgeteer is still Sling early and Omnigun later; I think I won't use the Mystery Ray if I get it. Priest will go Staff, getting the Staff of Doom (so that I use it as a weapon). Bishop will go Mace and Shield until I get a whip (which could be early (like before fighting the Monastery crabs), or it could not be until I reach Kunar/Sadok). I'm thinking I'll start the Bishop with Energy Blast instead of Frost; this allows Fire Magic to get some early skill increases. (I am still using the "no saving spell picks for higher level spells" rule.)
4. I haven't decided if I will go to Umpani Base Camp early or not. (By going here early, I could pick up spells like Fireball and Hypnotic Lure early, but then again, Hypnotic Lure is available (in Gadget form) in Trynton, anyway.)
5. Just for fun, I am planning on attempting to make heavy use of the Pray for a Miracle ability, and see how well that works.

Any advice on keeping my characters unencumbered?

If you want a character with stamina to burn then Dragon Lord | Valkyrie (start as Priest for higher Pie) is hard to challenge… I personally like Val for the melee axe action but go with whatever floats your own boat.

I've just checked Stamina consumption for the Renaissance Lute at different encumbrance levels. It has a massive influence:

white (none): 76
blue: 95 (+25%)
green: 114 (+20%)
yellow: 152 (+33%)
red: 228 (+66%)

This should be the same for gadgets of the same level (engineering vs music level). My guess is the percentages also look similar for other instruments of lower levels.

Edit: corrected an error

This mostly checks out with my results about spells. The way I expect it to work (percents compared to white) is:
white: 76
Blue: 95 (+25%)
green: 114 (+50%)
yellow: 152 (+100%)
red: 228 (+200%)

These estimates (based on my results of conventional casting) match yours, with the exception of the yellow result. Could you double check that figure?

By the way, you can specifically lower your bard's encumbrance by waiting until battle starts to equip your Rings of the Road; encumbrance is not rebalanced during battle.

I double checked. Your numbers are right.