Why is Friar Lawrence blameworthy for the deaths of Romeo and Juliet in Shakespeare's Romeo and Juliet?

Friar Lawrence is deserving of blame for the deaths of Romeo and Juliet because he is weak-willed and he has failed in his duty as spiritual adviser to follow through on the matters that he has said he would take action.

• Romeo and Juliet's marriage

After admonishing Romeo that "violent delights have violent ends,"(2.1) and asking him how he could so easily have fallen out of love with Rosaline, the priest agrees to perform the marriage ceremony because he does not want Romeo to sin, and because he naively decides that somehow a marriage between Romeo Montague and Juliet Capulet might unify the two feuding families:

In one respect I'll thy assistant be;
For this alliance may so happy prove,
To turn your households' rancour to pure love. (2.2)

However, he makes no plans to confer with the two sets of parents as, normally, the priest and spiritual adviser of a community would. Instead, it seems that he leaves the amelioration up to chance.

• Romeo's banishment

Friar Lawrence's idea for Romeo to go to Mantua is sensible; however, Friar Lawrence should have sent Romeo's servant Balthasar there periodically to check on him and advise him of the scheme involving Juliet. Had the Friar sent Balthasar to Mantua frequently with his messages, the servant would have prevented Romeo from ever believing that Juliet died. In addition, Balthasar would have discovered the quarantine of the city on another visit. Then, he would have reported this to Friar Lawrence, who could make different plans to prevent Romeo's misunderstanding of events.
If these visits by Balthasar were to have occurred, the actions of Romeo's purchase of poison and his coming to the Capulet tomb where he killed Count Paris and himself could all have been prevented. Consequently, Juliet would not have found him dead and then felt that she should kill herself.