Not new idea, but I like it.
I especially like Gorman's grid idea, but IMO changing shape of the grid would be better than trying to create weird shapes for each weapon to prevent taking more than one. (not to mention that how the duck SMG is 1,5x bigger than semi :P)
Something like this:

(13/12) White is your grid, every free block gives you +5% speed (up to 165%/160% speed with empty inv)
There are two version of the grid:
- first require taking weaker weapon (yellow) to take some of better sub-classes (green), but it makes difference between (red) and (orange) a lot less noticeable-only one slot less.
- second allows taking both (yellow) and (green), so less difference between (orange) and (yellow)
IMO first is better, because there is already big difference in how you use between (red) and (orange). and it could be changed even more by increasing size of (red) to 7 or even 8
(6) Red is for heaviest weapon (MG, RPG, andti-material rifle, mortar) it's supposed to prevent you from taking any real sub-class
(5) Orange is for main weapon (rifle, AR-currently called SMG, ect.)
(4) Yellow is for weaker main weapon (shotty, real SMG, ect.) You trade some of weapon properties for additional free space (less damage for example)
(3) Green is for sub-class item that you should own only one, or for good sidearm (medikit, body armour, adv eng tools, camuflage, MP, sawn-off)
(2) Blue is for weaker sub-class item or sidearm, when you want to be multi-class (weaker medikit, flak west, eng tools, pistol)
(1) Is for all small stuff. You can fit as many as you want, but you pay for each with speed (30 mg/ar/smg/mp/pistol ammo, 10 semi/shotty ammo, 5 anti-material ammo, 1 nade/rocket/mortar round, 10 blocks, 2 reinforced blocks, some smaller equipment like binoculars)
You can rotate weapons as you like.
Some of mentioned items are just example if we ever gets more items in game, don't discuss them here.
Weapon's sizes are designed for
balance, not realism.
Inv is dynamic (speed too), so you can enter it and drop item at any time (it stays on the ground for like half minute, fo ammo sharing), mined blocks slowly fill your empty space, players drop random single item when they die.
Amount of slots is ofc up to discussion, and can be easily applied to the grid.