Does the different ilvl actually matter on them? I mean, presumably they would have normalized stats at level 91-100.
Assuming similar ilvl transition from cata -> mop where ds raid finder ilvl (384 iirc) was the green quest rewards, the 3 tier heirloom weapons are either going to result in one extremely positively imbalanced weapon for the whole leveling process (heroic garrosh heirlooms), or one extremely negatively imbalanced weapon that you will replace (flex garrosh heirloom).
If they didnt normalize the scaling after level 90, they would have to balance around the most common heirloom quality (which will most likely be flex) and risk the heroic quality heirlooms scaling uncontrollably, making the entire questing process much easier than intended for a percentage of the playerbase. Alternatively, if they balance around normal or heroic versions, the flex version could very well end up underweight and be replaced early on.
Has their been a blue post explaining how this will work?
Would you rather the heirloom items were identical in growth from 91-100 or would you want them to remain three tiered for the entire leveling process? Why do you want your chosen preference?