I think that you use "brát si" when you are talking about a one person who is getting married to the other (the subject is singular - you can say "já si beru, ty si bereš, on (ona/ono) si bere [někoho]"), whilst "brát se" means that two people are getting married (the object is plural - you say "my se bereme, vy se berete, oni (ony) se berou"). You could also say "my (vy, oni, ony) si bereme (berete, berou) [něco]", but that would mean "we (you, they) are taking [something]".
SI is correct there. BRÁT can have both SI and SE depending on its meaning. BRÁT SI is to take something for yourself (or yourselves). Bereme si kousek dortu (we are taking a piece of cake). When you get two people taking each other for husband and wife (or wife and wife, husband and husband) it is the only case where SE is implemented. But only in plural. WE TAKE EACH OTHER = BEREME SE. If two (or more) people are involved in taking something like a cake, a car, it is SI. Even if the car is one and we take it for both of us.
When one of them is talking about taking the other person for a husband or a wife, it, again, is BRÁT SI. Because I am not referring to activity we both do, but to activity I do. BERU SI FRANTIŠKA. But JÁ A FRANTIŠEK SE BEREME.