By "Weapon Groups" are you referring to this section of the description?
"wielding two-handed small arms, heavy weapons, or super heavy weapons"
If so, then I suspect you're right, you'll have to make your own Custom tags, and assign them to replacement weapons. To do that, follow these steps:
Step 1: Define the tags.
Choose the class ability Recoil Absorption in the editor and scroll down to the bottom, where there is a "User Tags" button. Click that and you'll see every existing tag of the "Custom" group, which is a tag group we let users add to, for whatever purpose they need. Choose "New Tag" (its the first box at the top), then OK. Another window will pop up for you to define the New Tag, give it a unique ID and name that seem appropriate, like "HvyGun" for the unique ID and "Heavy Guns" for the name. Hit OK. Add another tag for the Super Heavy Guns. Then Reload your HL program with Ctrl-R or close and re-open.
Step 2 - Weapon Replacements
Go to the Weapons tab in the editor and New (Copy) one of the Heavy Guns you want this class ability to work for. Make a note of the original Unique ID. Place that original Unique ID in the "Replaces Thing Id" field, it's on the right side, underneath the 2 rows of blue buttons, and above the big grey window for author comments. Give your copy a new (but similar) unique ID. Scroll down to the User Tags button for this weapon, and add the appropriate Custom tag for this weapon (one of those you defined in step 1). Hit Test Now for your weapon.
Step 3 - Write the Eval Script
Go to the class ability Recoil Absorption, and use the eval script I gave you as a base, but change it to look for weapons with your new Custom Tag. Also change it so it applies a tag for using Str instead of Wis. Hit Test Now! once you think you have the eval script right. If it errors out, adjust the eval script appropriately.
Step 4 - Test with your replacement weapon.
Check and make sure it is working correctly with your first replacement weapon. If not, return to step 3.
Step 5 - Replace more weapons
Basically do step 2 over again, but with more weapons.
Step 6 - More testing
Once you've got weapons in there from each of the groups, test and make sure an example weapon from each group is behaving as expected. If not, back to step 3.
Step 7 - Dance the dance of accomplishment.
If you run into trouble, give it a couple tweaks yourself, and if you're still having difficulty, post here on the boards and I'll give you some more pointers, but I think this is within your grasp.