Leaving the info might seem confusing at first before you've realized that's what it's doing, but it's quite useful for a number of accessibility reasons. For example when moving the cursor around quickly and don't necessarily want to stop on a given cell, but can roll over it instead on the way to another target. Having it disappear unless you are currently on top of what you want to target is a very slow way to play, and you'll find yourself having to recenter over previous targets more often to make comparisons.
(Similarly the Scan window leaves old information until something applicable replaces that as well.)
I could look into adding an advanced option you can use to turn off this behavior and have it automatically disappear if you like, but you'll probably find that doing it that way has a lot of drawbacks, too.
Additionally, showing the per weapon target info in this case covers up useful game info, making it annoying to use Look mode to check weapons on the ground against equipped, since equipped weapon info becomes hidden and can't be shown again without exiting and re-entering Look-mode.
In this particular case I think a better approach would be to simply remove weapon targeting info while in look mode, and only show that while in the actual dedicated targeting mode. Are you using the mouse?