I've been wondering what is the purpose of life stone and found out that this is for augmenting weapon.

My question would be whats the difference between the levels?

Like for example what does the Lifestone with a level 46 vs level 49 or higher?

Is the level associated with the strength of the augmentation or is it the range on what grade weapon that you can use it on?

I haven't tried augmenting since I have to get a good weapon first because gathering millions of adena is not an easy task for me to buy a decent one from other people

Just level of skills.
The higher stone is 76 (I'm not counting with the 80, for S80), it you have luck and get a skill from then, you'll earn a skill lvl 10.
A stone of lvl 72, will give you a skill lvl 9.
Got it?

imo, I'm not certain if there's other things.

The bigger the lvl of the lifestone, the bigger the augmentation skill level (if you get an active, magic or passive skill). Top grade life stones are more likely to give skills, but they usually give weak stats (pdef, etc). High grade life stones have less chances of giving a skill, but they give better stats.

just to summarize:

-> higher level life stones give better active/passive/chance skills
-> higher level life stones give better stat bonuses(ex: evasion, pdef)
-> grade of life stone(NG/MG/HG/TG) affects the bonus given to the weapon/accessory

EDIT: by better skills, i meant higher level of skills...

yep higher level:)

Augmentation= pwetty wepan.

You forgot to mention what i said. Tg doesn't give great stats.

i think it is already part of "grade of life stone(NG/MG/HG/TG) affects the bonus given to the weapon/accessory"...

NG -> gives weak stat bonus
MG -> gives mediocre stat bonus
HG -> gives high stat bonus
TG -> gives a slightly lower stat bonus compared to HG

in fact, stats are almost the same, not depending the grade.
grade affect more the chance to get purple/red augment (wich means passive, chance or active skills)

level of the life stone determine level of the skill but some skills got max level with 2 different level life stone
for example, celestial shield is lvl 1 with a life stone 46 but also level 1 with a lvl 76 life stone.
clarity/empower/focus are maxed to level 3 and can be obtained with a life stone lvl 64

nuke skills are life stone level dependant, debuff too
(got an anchor level 8 with an ls 67 and a nuke lvl 10 with an ls 76)

life stones 80-82 dont augment skill levels (they are maxed to level 10 atm)

Exactly. But i wouldn't say slightly though.