Guild Wars 2

If I ran 2 sigils of leeching while wielding 2 1h weapons will I get the health buff from each weapon when they attack, say sword/dagger combo, or just from my first attack?

You only get it from one.. they share the same internal cooldown

Got it, thank you.

More than that, my personal testing has shown that only the sigil in the off-hand takes effect with a weapon in each hand. Even with two completely different sigils.
One simple way to test this is to place an on-switch sigil in the main-hand and an on-crit sigil in the off-hand. When you switch to it, nothing will happen, but you will get the on-crit effect. Switch the slots each weapon is in, and you’ll get the on-switch effect but not the on-crit effect.

This is just opposite to what I have observed. If you have 2 on-switch sigils on each of you main and off weapon. ONLY the sigil of main hand can be activated.
(I have hydromancer on my 1-hand sword and Superior Battle on warhorn, everytime I switch to S/H during battle, I can chill, but never get the might buff from Sigil of Superior Battle)

Grimwolf.7163:

More than that, my personal testing has shown that only the sigil in the off-hand takes effect with a weapon in each hand. Even with two completely different sigils.
One simple way to test this is to place an on-switch sigil in the main-hand and an on-crit sigil in the off-hand. When you switch to it, nothing will happen, but you will get the on-crit effect. Switch the slots each weapon is in, and you’ll get the on-switch effect but not the on-crit effect.