I think sometimes it is useful to think backwards. If you knew the product of the reaction is 2,2-dibromopropane, then what would that tell you about the electron availability of the propene? It may seem counter intuitive, but draw a resonance structure of the starting material using the non-bonded electrons of be bromine. If you protonate that resonance structure, what would the intermediate look like?
I too struggle with understanding this type of scenario. Bromine is a strong inductive electron withdrawing and it can be a (weak?) resonance donating group. Which effect should take precedence? If you replace the bromine with a nitrogen or oxygen, the same scenario exists, but those atoms are very good resonance donors and that chemistry predominates.
As a consolation, when this effect re-emerges in electrophilic aromatic substitution, you can use this principle again. Your chemical intuition should be rewarded to find that a bromobenzene will be less reactive than benzene. That is, bromine will still be a resonance donor, but because of its reluctance to do so, it will actually react more slowly than if the bromine were replaced with a hydrogen.