An answer from an actual Brexiteer (i.e. me).
I voted Brexit for 3.5 reasons (I was previously a europhile before I actually considered things in 2015)...
0.5) I actually bothered to read the Treasury and IMF reports rather than just the media headlines and the mean scenarios basically stated that the hit to annual GDP would be about 0.4%. I.e. average growth between 2018-2030 was forecast to be 1.8% rather than 2.2%.
This basically took away my largest concern since I took the view that a small hit to GDP was not something that would substantially impact my life and the potential existed for meaningful economic reform to overcome this.
1) Sovereignty - As somebody that had always had a strong nationalist leaning despite my prior europhile views I looked upon the number of directives coming from Brussels with dismay and found the idea of a foreign parliament or council directing our laws to be offensive. Notably there are conflicts such as the ECJ being able to overrule the Supreme Court, this is frankly offensive.
Identity was likely a factor here too. While I previously supported EU membership and federalism because of the potential power, I do not consider myself European and one only need look at the Franco-German betrayal and hesitation over Ukraine to see why we should remain sovereign.
2) Disagreements with various laws - I do not support VAT, I support things which would be tantamount to state aid, I do not support the common agricultural policy, I think an island nation allowing foreign states access to it's fish stock to be frankly insane and many others. Sufficed to say, my economic views do not wash with the level playing field.
3) The Refugee Crisis - Although the crisis itself is not a big factor in itself it embodies everything wrong with the current organisational structure of the EU. In 2015 we began to see a flood of third world migrants enter Europe and rather than defend the wishes of most European people in multiple states in multiple polls, we saw Merkel (previously a hero during the Greek austerity crisis) invite literally millions of third world migrants into the country.
Worse though, the European council led by Merkel and co then attempted to force states like Hungary and Poland which had explicitly expressed their wish that there be no migration allowed to accept a quota which would have forced more than 100,000 third worlders onto them.
What this told us is two things. The first is that as per the Lisbon Treaty referendums which were simply ignored and the states made to vote again and give the right answer, the European elite don't give a rat's about the opinions of their populous. The second is that they are not at all willing to defend the cultural makeup of Europe, inviting third world Muslims in their millions. No sane conservative who values the supremecy of market democracy and the liberties we have should support that.
In short, I am British and have more in common with North Americans than I do the Spanish and I find the idea that we should be dependent on their direction and are not capable of self rule to be offensive. Couple that with minor disagreements over refugee and economic policies and we see the reason for my change in stance. The attitude of the EU over things like NI only hardened my stance.