Are the HDI dimensions weighted equally?

The HDI assigns the same weight to all three dimension indices; the two education sub-indices are also weighted equally. The choice of weights is based on the normative assumption that all human beings value the three dimensions equally. The right choice of minima and maxima for the transformation of component indicators into indices gives more equal ranges of variation of dimension indices. Research papers that provide a statistical justification for this approach include:
Noorkbakhsh (1998). The Human Development Index: Some Technical Issues and Alternative Indices. Journal of International Development 10, 589-605.

Decancq, K. and Lugo, A. (2013). Weights in multidimensional indices of wellbeing: An overview. Econometric Reviews, 2013 - Taylor & Francis