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.
(assuming a literal Genesis interpretation) Genesis gives (to the best of my knowledge) no mention of a reason here. In the lack of further supporting scripture, "why not?" is probably as good a reason as any. Since no scriptural basis exists, one could just put it down to convenience: she was nearby and
The reason for Eve being tempted very likely has little to do with her gender. She was admiring the tree and the snake (Satan) tempted her. Non-christian apocryphal texts (there is a link here) often paint Eve as weak against temptation, but these documents are not accepted as canon by any of the major christian denominations.
Remember that Eve was created as a helper to Adam and created from Adam. As a being created from Adam, Eve would have, in a sense, been further removed from God.
Many ancient civilizations - including the one(s) to which the book of Genesis was written* - had the concept of emanations which basically subscribe to the idea that created things are subject to, and hence weaker than, the thing from which they are created. Adam being directly created by God would have been "closer" to God than Eve, and hence a "harder" target.
Note this isn't a physical, spiritual, or even a maturity thing. Its totally foreign to modern ears - its just the idea that Adam would have been "the firstborn of creation" and Eve wasn't. You don't attack the prince, you attack the prince's helper, and hope to get to the prince, and eventually the king.
*I'm a little bit concerned about opening a can of worms here. Did the Holy Spirit dictate the Scripture or was it a product of the cultures in which it was written? I actively don't want to open that can of worms. What I can say is this - the Jewish cultures to whom the Word was first given (whether that would have been as they were fleeing the Egyptians, when they were in the Kingdom, or as part of the Babylonian exile) all would have understood / subscribed to this concept.
I also get a little bit concerned, because while this concept is seen throughout Scripture, it is a mostly Helenistic idea, incorporated into the thinking of those who received the Word. If the writers of Scripture are simply human, then one would say this was simply part of the background of the writer. If the Holy Spirit is the sole writer of the Word, you could argue, hermeneutically, that he was simply conveying the information in ways that the people would have understood, or it simply could have been that's just the way it was.
I'm trying to stay objective and give an answer that is consistent with as many of these strains of thought as possible.
**N.B. The term 'logos' actually comes from this idea of an emanation - the Logos is the Word that was directly from God, was with God, and ultimately was God.
I am going to give an answer from a scripture-based Catholic point of view. The devil had no intention of making Adam fall. His full aim was to deceive Eve and Eve alone. This is the reason why Bible says that "Adam was not the one deceived; it was the woman who was deceived and became a sinner."1 Timothy 2:14
In revelation we know that all angelic beings' minds (including devil's) was illuminated by God with the plan of salvation, that God will be born of a woman: The woman will bring forth a child, who was to rule all nations with a rod of iron: and her child was caught up unto God, and to his throne.Rev 12:5 This is clear that a human being who is less than angelic beings, will be brought to higher glory than them. This human was to be brought forth by the woman. And the devil had a problem with this.
He knew that the woman was the central figure to this plan, and bringing down the woman will spoil the entire plan. The vision clearly states that the dragon was chasing the woman to kill her, seek his revenge and spoil God's plan. Rev 12:13-16 narrates his attempt. This vision happened before the creation of the material world.
After the creation of the material world, the Devil acted as soon as he saw a creature (Eve) who looked like in the vision he had before the fall, and decided to tempt her. The problem is he chose the wrong woman. Also note that the woman in the vision (before the fall) was timid and fearful. She runs for her life and earth has to protect her. The execution of devil's plan had cost the whole of humanity, not just the woman. So God cursed the devil/snake differently than He did with Adam and Eve. He foretells the victory of the woman and her seed and that they both will hate him. This shows that the woman will no longer be timid, but victorious.
Remember the war in heaven is not between God and the devil, but rather between creatures.
This is why Catholics believe that of all creatures Mary is the one Satan hates the most. His hate for all other creatures put together will not be equal to the amount of his hatred of Mary. Because when he sees Mary, he sees his loss and his doom.