For ranged weaponry: Perhaps every kill-shot over X difficulty would have a small chance of 'leveling up' the weapon to Heirloom status. The higher the shot difficulty, the better the chance.
( I realize online & c-RPG do not display shot difficulty, but I wish they did. I'm assuming it still tracks it, just without displaying it)
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As for everything else... I guess you would just have to use them a lot. So to 'level up' that expensive item, you actually have to use it. You can no longer simply let it collect dust, or buy it right before you retire at lv 31.
To prevent players from having infinite heirlooms, perhaps you can only keep as many heirlooms as you have Generations. Meaning, if you retire and your new guy will be Generation 6, you may then hold up to 6 heirlooms. When it levels up, it awaits your confirmation on the site to heirloom it. In this method, you could 'prime' a ton of items but wait until you've adequately retired to unlock them all.
I'd say once an item is 'leveled up' once, the default 'level up' chance for that item is drastically reduced. Meaning it's much harder to make it hit lv 2, and harder yet to hit lv 3. In addition to higher Generations holding more heirlooms, perhaps each Generation number increases your chance to level up items (albeit barely)
I realize this makes it sound like Heirlooms would be more common instead of more rare, so the level up chances would have to be really low, as well as have pre-requisites (like the ranged shot difficulty). I can't really think of any good ideas for non-ranged weapons or armor, and even if I did they'd be too farmable. (Probably better to keep them secret)
Edit: If chadz, or whoever would program it, likes the idea and wants more thoughts, I'd be glad to brainstorm in private.