LogP of halogen derivatives of aromatics and aliphatics explanation
Here is a chart of the solubility of the species in water and the log of the partition coefficient you noted. 

                           solubility       solubility
                  MW       g/100ml water    moles/liter   log(P)
  Benzene         78.11    0.179 (1)        0.0229         2.13
  Flororbenzene   96.103   0.155 (2)        0.0161         2.27
  Cholorbenzene  112.56    0.050 (2)        0.0044         2.84
  Bromobenzene   157.01    0.041 (2)        0.0026         2.99


(1) Wikipedia

(2) Cation Complexes of Compounds Containing Carbon-Carbon Double Bonds. VI. The Argentation of Substituted Benzenes
L. J. Andrews, R. M. Keefer
J. Am. Chem. Soc., 1950, 72 (7), pp 3113–3116
DOI: 10.1021/ja01163a085
weblink http://pubs.acs.org/doi/abs/10.1021/ja01163a085

There is a Wikipedia chart in article on Ionic radii. 

 Ion     radii (picometers)
  F-      119
  Cl-     167
  Br-     182


The halide on a benzene ring is going to be relatively covalently bound. It definitely won't dissociate to form ions and only very moderately participate in hydrogen bonding. 

So as the size of the halide increases the "volume" of the molecule increases. Thus the molecule would preferentially like to be in the non-polar phase. 

Here is a scaled image of fluorobenzene molecule:



and a scaled image of the bromobenzene molecule.



Haloalkanes

The "anomalous" fluoroalkane is explained in a different manner. To get an n-alkane that has a boiling point above room temperature we need to go to n-pentane. 

                   BP                 solubility      solubility
                   (deg C)   MW       g/100ml water   millimoles/liter
 n-Pentane         36        72.15    0.040 (1)         0.55
 1-Fluoropentane   63        90.14    1.270 (2)         14.1  
 1-Chloropentane  108       106.6     0.197 (3)         1.85
 1-Bromopentane   130       151.05    0.127 (4)         0.838


(1) Wikipedia
(2) NIH
(3) Wikipedia
(4) Handbook of Aqueous Solubility Data, Second Edition
 By Samuel H. Yalkowsky, Yan He, Parijat Jain

There are two competing effects.

(1) The size of atom bound to the alkane. 


  
    Br > Cl > F > H
    
    Scaled model of Fluoroethane
  




(2) The second effect is the electronegativity of the X group in the $\text{Alkane}\text{X}$ bond. 

 F    &gt;   Cl   &gt;   Br   &gt;   H
 4.0      3.2      3.0      2.2


The fluorine atom has a slightly larger radius in a fluoroalkane than the corresponding C-H group. But the halide groups allow more dipole forces. So by "volume" the overall effect is:

 fluoroalkane
 alkane
 choloroalkane
 bromoalkane