The main problem here is not that one or the other are inaccurate but the fact that both methods show completely different things that have never been and will never be “compatible” - for lack of a better word.
AMR shows the best combination of items through calculations of millions and millions of different gear sets. While a specific item might not be optimal in every respect, combining it with another item can be better than using two “optimal” items due to the complexity of stats and their interactions.
Stat Weights tell you how much DPS you will gain if you add stats on top of your currently equipped gear. Most of the time differences between stats are relatively small and will change with every new item causing different suggestions. Thus, Stat Weights can’t tell you if an item is universally better than another item because that’s not what they’re intended to show.
Let’s take critical strike chance as an example: If you absolutely need to get 100% crit and manage to reach it, additional crit will be worth nothing anymore. Your Stat Weights will then have a value of 0 for crit - which is correct, because having more crit does literally nothing for you.
Importing those weights into Pawn will now show every single item with crit as bad, because one of the two secondary stats is worth nothing. Does that mean that every item without crit is better than what you’re currently wearing? Obiously, it doesn’t - because when using that item you would drop below 100% crit which would be bad in this example.
AMR’s Best in Bags would then still recommend the item with crit which would be the correct decision.
Of course, that’s an extreme and frankly unrealistic example but it does show the differences between those two ranking systems - and why using them in conjunction is more diffcult than you might imagine.
In practice the differences are extremely small but that just increases the complexity of making optimal gearing decisions because even a couple mistakes while playing might have a bigger impact than say having 50 crit or 50 haste.