Weakness specifies that you may "play the first enhancement in battle." There can only be one first enhancement. Therefore, when you block with The Jeering Youths, his ability activates prior to Weakness triggering. Therefore, you can either choose to play an OT brown enhancement with him, or choose not to do so, do to his "may" ability, and simply play the first enhancement via Weakness. The latter would enable you to play NT enhancements as well. However, if you play via The Jeering Youths, you have already played the "first enhancement," and Weakness no longer does anything.
Kirk