OnTrigger and Input.getkey on picking up weapons from the ground.

try adding a rigid body, and ticking the gravity off, sometimes, you'll need to have these on triggers to make them work.

( even with the more common mouse over methods )

You don't need OnTriggerStay2D to repeatedly set a bool every frame - it would be more efficient to use OnTriggerEnter2D. Please post a screenshot showing your collider/rigidbody settings applied to each object.

Use The OnTriggerEnter / Exit. Additionally, you may pass over more than one weapon, or pass over a weapon immediately before a non-weapon.

In the latter case, your code would evaluate OnWeapTrig to false, despite you standing on a weapon.

You might have a few issues in the second statement, but without any extra explanations we can't help too much there:

 // Keep track of the weapons we're in range of
 private List<Transform> nearbyWeapons = new List<Transform> ();
 
 // This will be called whenever you enter a trigger collider
 void OnTriggerEnter2D (Collider2D other)
 {
     // Check if this was a weapon
     if ( other.CompareTag ("Weapon") )
     {
         // If so, add it to our list
         this.nearbyWeapons.Add (other);
     }
 }
 
 // This will be called whenever you enter a trigger collider
 void OnTriggerExit2D (Collider2D other)
 {
     // Check if this was a weapon
     if ( other.CompareTag ("Weapon") )
     {
         // Check if we had this previously, and if so remove it
         if ( this.nearbyWeapons.Contains (other) )
         {
             this.nearbyWeapons.Remove (other);
         }
     }
 }
 
 // Your pickup function
 public void OnWeaponPickup ()
 {
     // Make sure we were standing on something
     if ( this.nearbyWeapons.Count == 0 )
         return;
 
     // You can choose what to do here for determining which weapon to use
     Transform weapon = this.nearbyWeapons [0];
 
     // Possible issue?  If your weapon is full, it looks like you are
     // trying to remove the current one, but then this statement will 
     // do nothing else following that?
     //
     if ( IsHolsterFull () )
     {
         DestroyWeaponInCurrentSlot ();
     }
     else
     {
         if ( currentWeapon != -1 )
         {
             DisableWeapon (currentWeapon);
         }
         currentWeapon++;
     }
     EquipWeaponInCurrentSlot (weapon);
 }