Your weapons and armor plays a huge role in how well you will be doing when playing The Outer Worlds, and if you find a nice weapon or armor that you really enjoy, it might be worth considering to just upgrade these instead of looking for a replacement. One of the benefits to this is that great weapons and armor can be worn for much longer, so if you really enjoy a particularly useful legendary item, upgrading it will allow you to keep using it even if the DPS starts being on the low side.
Each time you upgrade your armor or weapon, it will gain one level. You can only upgrade each weapon or armor to match your current level, so you won't be able to farm Bits and get a weapon to level 35 while you are still in your 20s. However, if you keep upgrading your gear to match your level, then you should be in a good position to tackle the challenges presented by the game.
In order to actually upgrade your weapons and armor in The Outer World, you will need at least 20 Skill Points in the Science Skill. This is easily achievable even at a very low level. Anyway, with at least 20 Science Skill points, you will get the Tinker ability, which allows you to upgrade weapons and armor.
In order to actually upgrade it, you will need to find a Workbench. These are found in most of the bigger settlements and cities, and there is even one aboard the Unreliable in the main cargo room.
When you are at a Workbench, interact with it and choose the submenu called "Tinker". Select the armor or weapon you want to upgrade and hover over it to see how many Bits it cost to upgrade it one level, and how much of an improvement it gets. It is gradually more expensive to upgrade weapons as they get to a higher level, and high-level weapons and armor is actually very expensive to keep to your own level, especially if you want to upgrade all four weapons and both slots of armor each time you level up.
And that's pretty much all there is to upgrading weapons and armor in The Outer World. It's a very convenient method to keeping your gear useful for a much longer time, and definitely something we recommend if you find a weapon or armor that you enjoy playing with.