It can be incredibly high, +7 is far from the limit.
However, +3 is the most "popular" enchantment level people go for at a lower level.
At the moment, pretty much everyone lvl64+ is aiming for +5 weapons atleast, and some people are aiming for +7 or +9.
Other than that there has been a few +10 to +14 weapons around every now and then
Btw, 7 elixirs has a greater chance to fail +3 than success.
You should try 10-15 elixirs to be sure.
and
dont do +1 without lucky powder, it wont help you gain +3 it will only make chance of you wasting a elixir at +1 high +_+