Why did the devil tempt Eve first? Why did the devil go after Eve and not Adam?
Was it because Eve was weaker than Adam?
Why didn't the devil tempt Adam first?
It must be noted that the Bible never explicitly answers this question, so our answer has to come from related observations we make from the text.  However, we must admit that these observations are not explicitly taught from the Scriptures, so we must not be emphatic where the Scriptures are not.  It is important, then, to identify what it is that we do know and what it is that we do not know.

We do know that the prohibition from eating the fruit of the tree was directly given to Adam by God prior to the creation of Eve.


  15 The LORD God took the man and put him in the garden of Eden to work
  it and keep it. 16 And the LORD God commanded the man, saying, “You
  may surely eat of every tree of the garden, 17 but of the tree of
  the knowledge of good and evil you shall not eat, for in the day
  that you eat of it you shall surely die.” 18 Then the LORD God
  said, “It is not good that the man should be alone; I will make him a
  helper fit for[e] him.”  Genesis 2:15-18 ESV


The Bible never indicates how Eve learned about the command.  We do not know whether God repeated the command to her after He created her or whether Adam passed it on to her.  We do know that she seems to be aware of the command during the temptation, although her statement of it differs from that which was given to Adam--Eve adds the part about not touching it.  She also fails to call the Tree of the Knowledge of Good and Evil by its name, referring to it simply as the tree in the middle of the garden.

So, perhaps Eve received the command secondhand and wasn't as certain about it as Adam was.  Again, we don't know for sure, but this is at least a possibility.  If so, then it is reasonable to assume that Satan saw Eve as the one more susceptible to deception.

We do know that by deceiving Eve, though, that Satan got two for one.  He had to deceive Eve, but Adam willingly followed her into sin, despite not being deceived.  Eve seems to not have understood what she was doing, but it seems that Adam actually did--and did it anyway.


  "and Adam was not deceived, but the woman was deceived and became a
  transgressor."  1 Timothy 2:14 ESV


If Adam had been the first to sin, we do not know if Eve would have followed.  Perhaps so.  We do know, however, that Adam did follow Eve into sin.

It could be suggested that Eve's weakness was uncertainty, while Adam's weakness was Eve.

So, again, we don't know for sure, but we can make some observations about the text and draw some possible explanations to answer this question.