Was lazy to read the whole thread (just stumbled upon it), but that's my hero weapon summary in which I made a few corrections meanwhile (corrected it in the quoting).
As an explanation to Shingen burst buff note, as you may know, each rarity has its own burst multiplier & burst buff is additional with that. So while the damage gain in number stays the same, the relative gain (expressed in %) varies depending on the already existing multiplier.
There's also an introduction part which is probably useful for those new to hero weapon stuff or for people with lacking knowledge on hero weapons. Gonna add it here:
Each hero has 2 types of weapon: atk & hp. Atk will give you 30% elemental atk bonus of the corresponding element at SL20 and hp gives 30% hp.
Every hero weapon has a 2nd, hero specific effect that will boost one of their abilities.
Note that these effects only work with the corresponding hero and only if equipped as main weapon.
Atk & hp weapons for the same hero share the same burst effect.
Note that the burst effects described below are only for MLB weapons: at 0* they won't have any kind of burst effect, then the effect will increase as you proceed with LB.