The situation with Br2 dissolving in water (if we assume it stays Br2 and doesn't ionize) has more to do with an entropic effect than it does with the bonding. Even methane will dissolve in water to some extent (3.5 mg/100 mL) despite the very weak bonding between methane and water.
In order to understand why this is, imagine a container separated in the middle by a removable barrier. In one half of the container you fill it with only blue spheres and in the other half of the container fill it with brown spheres. Once you remove the barrier and shake up the container for awhile, you might suspect that the two sphere colors become less and less separate from each other and more and more mixed together. This is due to an entropic effect. The probability of the two colors separating from each other on each side after shaking is much lower than the probability that they will be all mixed up.
Now we do the same experiment, but this time we attach the blue spheres to each other using heavy duty tape (this tape will symbolize "strong bonding" between blue spheres for one another). When we pull out the barrier and shake it up, we might expect that all the blues will now stay together due to the tape and that this would keep them separated from the brown balls. And for the most part (if we did a good job taping), we might be right. But you wouldn't be surprised if at least *some* brown balls got mixed in with our taped blue mass after shaking perhaps because there were parts where the tape weakened long enough to let them leak through or for some other reason. The point is that without the tape they would tend to mix completely but with the tape they will still "want" to mix but will be inhibited for the *most part* (some will still leak through). This is how even some methane gets dissolved in water despite the weak bonding for water and methane. Not a perfect analogy, but for now it will do.
For Br2, this is a factor that allows it to dissolve as well. Br2 is a bad example to use though, because it does not stay Br2 in water forever, but rather it is ionized by water to H+ and Br- in solution. Hence, it's solubility is higher than you would expect from other non-ionizable compounds with poor solubility in water such as N2, O2, and CH4 that are far less reactive towards water.