I am having a little trouble deciding what enchantments I want to use for my Fine Steel Bow...
I have chosen drain speed 100% for 1 second as it seems to reset an enemies detection,allowing me multiple sneak attacks.
Soul trap of course.(Azura's Star)
I would like to use absorb health 10pts for 2 seconds,does weakness to magic amplify absorb health in any way?(magnitude or duration)

Don't put absorb health on your bow - it will only work when your bow target is within melee range, rendering it useless.

Your drain speed 100x1sec + soul trapx1 sec is excellent. Add some elemental damage for one second and you are good to go.

I would not try to get fancy with weakness to x on a bow. Just add poison to the bow above. When my archer uses weakness (to poison in her case) before a bow shot, she uses a spell to apply the weakness.

I did not know that...but I would like to know if weakness to magic amplifies the magnitude or duration of absorb health,as I use it on my sword.

It amplifies magnitude, afaik.

How about weakness to magic amplifying damage health in any way?(magnitude or duration)

Weakness to Magic impacts every type of magic including itself. Check UESP wiki for extensive info about how weakness effects work together.

Actually, an ideal set up is Soul Trap + Weakness to Poison + Weakness to Magic, and then Soul Trap on a second bow. Be sure the first bow has at least 4 sec duration for the weakness effects. You shoot the enemy with the first bow. You can shoot several times. The weaknesses stack up with each shot (unless you miss, of course). Anytime you feel you have sufficient multipliers for damage, poison the second bow and ... well, dead enemy.

Do not poison the bow with WtP on it because the game resets such a weapon's poison to 1 regardless of strength of said poison.

the 'weakness too' effect wil not amplify the magic in the same spel. so you need to hit your target a 2nd time to get advantage of the weakness too magick spell.

Yes, that's why I said shoot the target several times.

However, to be completely clear, the WtP will effect the target even with the first shot. So will the WtM, but the WtM with the first shot will not do anything to the WtP on that shot. However, if you hit the target with a spell or hit it with a poison after shooting it one time, either effect will be triggered (within the time duration, of course). If you continue shooting it with WtP + WtM, you will easily multiply the impact of your eventual final shot. One hit kills even against tough enemies.