The simplified formula for debuff.

base / ( 1 + <effect total> / 100 ) == net value

Damage resistance formula is a might more complicated but works similar to the debuff formula above. Damage resistance is a curve approaching 75% which is the theoretical cap. The sweet spot for damage resistance is around +180 armor which is around 60% damage resistance. After +180 the extra damage resistance you get per armor points really starts to drop off.

The formula and a nice chart from STOked 76 is at STOWiki

Damage Resistance
The simplified formula for buffs is

base x ( 1+ <buff total> / 100 ) == net value

Weapons have a lot of buffs which affect the weapon damage, there are a couple of "strengths" (as Geko calls them) based upon the Tier of the Ship and the Mk of the weapon. (Examples given by Geko is a T5 ships strength is 1 (+100) for the formula) and strength for Mk X weapon is 1 (+100).. Then you have the factor which is your Captain Weapon skill which can make +99 at rank 9/.9 for every stills. And then finally is the factor for weapon consoles.

For weapons the formula would be (and assuming weapon power of 50).

base damage x ( 1 + <ship strength> + <weapon strength> + <skill total> / 100 + <console total> / 100)

Plugin in some real numbers Mk X weapon on a T5 ships with weapons skills at rank 9/9 and 5x +26 disruptor weapon consoles (go Bortasqu' War Cruiser).

base damage x ( 1 + 1 + 1 + .99 + 1.30 )

The bottom line is that Weapon Consoles are only providing 20% of the overall base weapon damage. Weapon consoles can and do add a decent chunk of extra damage. And that why adding 5x +26% weapon consoles doesn't boost your base damage by x2.3