So looking at Jisho.org, I think that you are looking for definition 3 (consequence; result; effect).
My translation is very close to yours:
It is said that the usage of soft obi(s) has increased by 30% since last year, a result that comes from the fact that many young women cannot tie a stiff obi.
Yuuichi Tam's comment is very pertinent, you can also translate that as 'Because,' but ため has a more formal context than から/ので。 The reason you may have difficulty finding that translation stems from the fact that English has phrases that have similar meanings to
because. Check the link for examples. The truth is that ため is more formal and would be better translated to
by reason of ___ of only just to keep the formal feel. If you don't care about formality quite as much, just plain
because is adequate, and 100% accurate.
Retranslating that sentence using
because we get:
Because many young women cannot tie a stiff obi, it is said that usage of the soft obi has increased by 30% since the last year.
Hope it helps.