This is a short, abridged version of a discussion just had on the Discord.
Give the WEXP status screen numerical values, and not just pixel bars to represent progress to the next rank. This can be a % counter to the next rank, or actual numerical value. This can be optional if the other two solutions below are done instead, since this might look ugly and jarring.
When you gain EXP at the end of every fight, also show a WEXP bar above the regular EXP bar ticking up, or a MAX! if that rank is maxed, similar to how FE13 does for EXP. You don't want to pause the game to show WEXP ticking up, which is why I say it should show the bar going up at the exact same time as regular EXP.
When you gain a Wlvl, all you see is that your equipped weapon rank goes up. Change this to show what the new rank is. So "[Icon] level increased to A rank." as an example.
Why bother making these changes? WEXP is a very passive thing in GBAFE. If you aren't paying attention, you might not even realize a weapon, like the Devil Axe, is giving you absurd amounts of WEXP. You also might not realize a weapon is giving you zero WEXP. Often a player may get the "Weapon level gained" dialog box during an enemy phase, and by the time their phase rolls around they've forgotten about it.
A fourth option is to also show in a weapon's description how much WEXP a weapon gives. I think this is optional, and it might make the weapon stat box rather ugly, but if it could be added, that would be neat.
Edit: Tequila fixed this.