I think that hardcoe Mode should add weight to everything, even caps. (0.01 weight = 100 caps = 1 weight.)Hell, even quest items. (With the option to drop them though, and a pop up that tells the player it is a quest item and it might be important.)
Bethesda made quest items and characters be flagged as undroppable and essential, respectively, because of problems that people complained about from Morrowind: Not being able to "beat the game" proper because a certain item got lost or because a certain key character was killed (either by the player or other means). Rather than deal with new sets of complaints and so forth, Bethesda basically started implementing this practice with Oblivion, and continues on. Items could otherwise get lost because of a physics glitch or interaction (falls through the mesh of the floor, or what sometimes happens when I bump into a crate, get knocked wildly off in a direction, sometimes flying for what would be measured in miles in the game, to land in either an unreachable place and remain there, or otherwise be generally unable to be found again in that playthrough).
They wanted to avoid the problem of players breaking the quests and making the game unable to be completed in proper fashion (beat the main quest, and side quests as desired, and so on).
But yeah, I think in the first Fallouts, even caps had a weight to be taken into account when loading up on gear.
0.00 is not weightless, they are just too light to display.----is weightless, but mostly quest items.
Yeah, even the "weightless" coyote tobacco leaf adds up to a pound, granted takes around 100 or so to make that single pound of carriage. The only truly "weightless" items are the ones that don't show a number for the item weight.
Ammo weight made hardcoe mode annoying. I was carrying bare minimum ammo, and when I switched it off I lost almost 200 lbs of equipment.
Maybe you should stash some of that somewhere in a safe location and free up some of your inventory space. I have several thousand pounds' worth of ammo with my character, but I only ever carry around maybe 10 pounds altogether, depending on what loadout I choose to go with for my excursions.