At level 80, I skipped Cataclysm and went straight to Pandaria. Even as my warrior leveled up, and that heirloom axe increased in iLvl along with me, Dugi still ranked that iLvl 87 sword higher. I kept picking up new 2h weapons, and Dugi kept rejecting them in favor of that Wrath sword. That's when I noticed that all of these Pandaria weapon drops, even weapons 20 iLvls higher than the Wrath sword, had secondaries under 20. So even though Dugi Gear Advisor is showing that a new weapon would provide a DPS increase, it still prompts me to re-equip that Wrath sword every time I equip a new weapon. Meanwhile, I've kept the heirloom axe in my bags, assuming that at some point its stats would once again beat whatever I had equipped, but nope, it doesn't, according to Dugi.
Heirlooms are special pieces of armor that level up with your character, so they have stats that are always respectable for your character’s level (up to level 110). Heirlooms that fit the head, shoulder, chest, legs, and back armor slot offer an experience bonus. The total bonus is 45 percent if you have them all. It’s also possible to acquire a ring that adds another 5 percent, but you must win a fishing contest acquire it, and that can take some time.