In the screen where you can arrange the troops inside a dropship, you can see the available troops on the bottom. You should also be able to see what their primary weapon is, but that part falls just off the screen.

I'm playing in 1920*1080 on a 24" screen (I assume a default resolution for many widescreen 24" LCDs).

Full screen:

WeaponDescOutOfPlace.jpg

Zoom of section:

WeaponDescOutOfPlace02.jpg