Do bullies pick on sociopaths? As a percentage of their endeavours, do those with a tendency to use bullying focus more or less on sociopaths as a per capita of their targets?
As a percentage of their endeavours, do those with a tendency to use
  bullying focus more or less on sociopaths as a per capita of their
  targets?


Thanks for this interesting question. Based on my research the short answer appears to be that there is no clear evidence either way. The longer answer is that this is probably too complicated a question to easily answer. 

Explanation

Based on psychology today I take sociopaths to be those who have: 


A disregard for laws and social mores 
A disregard for the rights of others 
A failure to feel remorse or guilt 
A tendency to display violent behavior


It is also important to consider that sociopaths develop these traits rather than being born with them, like psychopaths are (see quote from psychology today 1). 


  Psychopathy is related to a physiological defect that results in the
  underdevelopment of the part of the brain responsible for impulse
  control and emotions. Sociopathy, on the other hand, is more likely
  the product of childhood trauma and physical/emotional abuse. Because
  sociopathy appears to be learned rather than innate, sociopaths are
  capable of empathy in certain limited circumstances but not in others,
  and with a few individuals but not others.


The literature on child bullying suggests that both bullies and victims tend to be more likely to have psychiatric disorders, such as sociopathy. The rates are 13% for bullies/ 8% for victims {1}. This suggests that 92% of those who are bullied are not sociopaths, but it fails to control for the fact that fewer individuals have sociopathic tendencies at that age. What is really needed is a test comparing two samples of children, on with sociopathic tendencies and one without.

An additional complication with this question is that it may be the case that children become sociopaths due to being bullied rather than being bullied because they are sociopaths {2,3}

Indeed some research {e.g., 2} suggests that anti-social personality disorder (which includes sociopathy) is the most common disorder amongst victims of bullying.

I hope this answer has been useful. Please let me know if you would like more information or need clarification on any points.

References:

{1} Copeland, W. E., et al. (2013). "Adult psychiatric outcomes of bullying and being bullied by peers in childhood and adolescence." JAMA psychiatry 70(4): 419-426.

{2} Sourander, A., et al. (2007). "What is the early adulthood outcome of boys who bully or are bullied in childhood? The Finnish “From a Boy to a Man” study." Pediatrics 120(2): 397-404.

{3} Arseneault, L., et al. (2010). "Bullying victimization in youths and mental health problems:‘Much ado about nothing’?" Psychological Medicine 40(05): 717-729.