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If I create a weakness to poison 100% for 20 seconds or similar, then conjure a mace, put a 5 damage for 10 seconds poison on it, would it do 10 for 20 seconds or only improve the damage and not the duration?

When the damage has a magnitude value (if you can adjust its strength at all) then I believe the weakness effect will increase the magnitude alone: the poison or spell damage becomes stronger. Same time limit, just the strength increases.

Only if the effect is an "all-or-nothing" deal, such as Invisibility or Paralyze, the weakness effect will increase the duration instead. Since you can't make such spells any stronger, the increase effectiveness has to come in that way instead.

Does anyone know if I stack weakness to poison + magicka a lot, and then hit the target with a burden poison, will the target become over-encumbered?

it can, but damage strength would probably be more effective and more permanent

Damage Strength would probably be my first choice.. right now I can't remember one ingredient with this effect, is it difficult to produce such poisons? Burden is easy, cause the ingredients are easy to get..

I'm fairly certain that using a spell with effects:

weakness to poison 100% for X seconds
weakness to magicka 100% for X seconds

multiple times on an enemy will stack the weakness to magicka, so the following WtP will be multiplied because of WtM.
I killed a Grumite Deathdealer with a simple 1-effect damage poison in a matter of seconds, after casting the spell on him several times.

Since Burden effect is easier to find on ingredients (at least for me), I can generally create many more burden poisons than damage strength or speed. That and I've read on (a) forum that weakness to poison does not affect magnitude of Burden, but the durationn; I find that hard to believe..
I'll test all this the next playing session, as I didn't have time yet. :p

Damage Speed didn't do squat in Morrowind, but maybe they fixed it for Oblivion.

Here are the ingredients for Damage Strength along with the requisite Alchemy skill level to access that effect.

Bread Loaf(75)
Leek(75)
Primrose Leaves(75)
Tiger Lily Nectar(25)

Bread and Leek is about as common as you can get, and alchemy yields the following max result.

Damage Strength
(Max Mag=3,
Max Dur=12,
i.e., 36 points damage)

So you can get 36 points of Damage Strength from just one application before any modifiers from Weakness to Magic or Weakness to Poison.

With 100% of both, the Weakness to Magic should make the Weakness to Poison 200% effective so that’s 36x3=108 points, meaning if they’re carrying anything with any weight they will be over encumbered.

@Logansrun
How did I possibly miss Bread and Leek!? Tnx for the tip!

I was brewing some damage fatigue poisons lately for the same purpose and find it quite effective (and funny)

No problem, but Damage Fatigue is only temporary. Of course, if you finish them off while they're passed out on the floor, then I guess that makes it pretty permanent.

I'm playing the latest official version + l.a.m.e. mod, so I can't say if this is true for any version:

Damage fatigue continues to have effect even if the target inflicted by it has 0 fatigue - it goes into negative numbers.
My self made spell backfired once when I targeted a Lich and he reflected it - I dropped on the floor and was lying there for about half a minute.
I realized my fatigue was around -200.. it was like a super paralyze spell! I barely survived this funny situation

Having an NPC (or your character) "faint" when Fatigue goes negative is a feature present in the vanilla game. Wear two items enchanted with Damage Fatigue, and your character will not regenerate their Fatigue even when standing still, if you wanted to roleplay a character who needs food to replenish themselves.