The inventory is a complicated beast to work with, but I will try my best to explain:
Your inventory is based on Weight and Pockets. The reason why you can't get the hatchet into your inventory, is because you don't have a pocket available to put it in, so your stuck with holding or dropping it. A lot of people have confused the top right numbers as "slots." This is not the case. The top right number is how much weight that piece of baggage or clothing can carry.
Pockets: Each piece of Clothing. or Baggage, has a certain amount of space/pockets. You will only know how many pockets each clothing has by putting items in until you can't insert anymore. (That's the only way to my knowledge on how to find this out.) For you to freely move items around, back and forth, or properly use your hot wheel/bar, you must have at least one open pocket to work with. Be sure to check how many pockets you have, and keep some open pockets available when using your hot wheel or switching items. Feeling ALL your pockets, will force you to have to hold or drop the item in your hands, because that is the only available place for it to go.
Weight: Each piece of clothing, or Baggage, has a certain amount of weight that it can withstand. For a piece of clothing, or Baggage, It shows how much weight it can hold at the top right. For each actual ITEM, like a can opener, the top right number shows how much it weighs. I know that sounds confusing, and it is. So think of it this way, CLOTHES show how much it can hold, ITEMS show their weight. That's as simple as i can put it. (If you want to see the actual weight of your clothing or backpack, look at the very top of your inventory screen, where it shows all your equipped clothing, that number at the top right, on that specific equipped clothing bar, shows how much the actual piece weighs.) No matter how many pockets you have, you still have to abide by the weight limit of each piece of clothing.
Micromanaging: To micromanage your inventory, press and hold A button on the item you want to move, and press RT or LT to move it to the desired piece of clothing. You can not individually move the item side to side. You can only micromanage items by moving them from clothing to clothing. (or bags) Try to fit certain items in certain pieces of clothing or bags so you can be sure to utilize every pocket, and also abide by the weight. Small items in pants or shirt/jacket, while larger items can go into your back pack, or tactical vest.
Its super complicated, and I understand they are going for realism here. I feel the inventory idea here is actually not a bad idea, buts its easily dis functional when the guns bug out and don't reload properly, or when items disappear suddenly (which could be in cooking pots, protected containers, or medical bags). It would literally take someone extremely OCD (Like me) to be able to organize this system to the fullest and understand the true functions behind it, but for gaming, it is much too complicated and frustrating to deal with. So i wish they pick one or the other. Pockets or Weight. Not both.