發 and 髮 have been simplified into one single character: 发.
发 contains the separate meanings of 發 and 髮 but differentiates by tone: fa1 (fā) and fa4 (fà).
Most topolects (西安，武汉，洛阳，乌鲁木齐，贵阳，济南，柳州，万荣，etc.) don't have a tonal differentiation and 发 only has one pronunciation.
What is the origin of the tonal differentiation in Mandarin?
We might never know the real reason. All those rime books indicate that 發 (out) and 髮 (hair) are always the same pronunciation, and both are entering tone (入聲). This means there is a terminal -t in pronunciation on 發 and 髮. We know that when -t was lost in Mandarin and the tones became unstable. In Chinese phonology it is named 派入三聲. The entering tone (入聲) was gone and all characters in entering tone go to the rest three tones, namely the flat tone (平聲), the rising tone (上聲) and the leaving tone (去聲). In this way, it is possible that 發 and 髮 develops different tones in Mandarin.
The two characters pronounce the same in some dialects may be a coincidence. I come from Xi'an, you are right, we really read 发 in 头发 and 发展 in same tone. But there are also characters with different tones in our dialect, but the same in Mandarin. Dialect does not necessarily correspond to Mandarin one by one, it usually has its own rules. The tones of most characters in northern dialects correspond to Mandarin one by one usually, but not all of the characters. Comparatively, the tones of most southern dialects are not regular like northern.
