Now we discuss about this and I see in my equipment list that my 3x Great Axe (a.k.a "Titus My Best Friend", the weapon I use the most) has a little sister:
Mighty Great Axe
weight 4
requirement 14
spd rtng 95
weapon length 96
swing damage 49, cut
thrust damage 0 pierce
Sell for 3,247
FYI, my normal Mighty Great Axe:
weapon length: 96
weight: 3.5
difficulty: 15
speed rating: 95
weapon length: 96
thrust damage: 0 pierce
swing damage: 46 cut
Sell for 6,612
Obviously the cheaper sell price could indicate a lower upkeep cost (but I cannot confirm) but the thing is that I cannot select it when I play: there is just one Great Axe, the normal one, in the list (but I have also too much gears and many stuff don't appear in the list, that might be the reason).
My theory is "THAT" could be the compensation to the last heirloom buff: some stats boost when playing.