How does the energy of non-resolved spectral lines get distributed in an FFT?
As The Photon says, how the energy spreads is out is determined by the window function you use. Here's an excerpt from The Scientist and Engineer's Guide to
Digital Signal Processing, chapter 9 (near the end):



Your choice of window function will largely depend on what about the signal you are trying to measure. Do you need high frequency resolution? Do you need accurate amplitude measurement? It's not possible to optimize for everything at once.

From your comments, it sounds like the flat-top window may be most appropriate. Again, from the guide:


  This leads us to the flat-top window, shown in Fig. 9-5d. In some applications the amplitude of a spectral peak must be measured very accurately. Since the DFT's frequency spectrum is formed from samples, there is nothing to guarantee that a sample will occur exactly at the top of a peak. More than likely, the nearest sample will be slightly off-center, giving a value lower than the true amplitude. The solution is to use a window that produces a spectral peak with a flat top, insuring that one or more of the samples will always have the correct peak value. As shown in Fig. 9-5d, the penalty for this is a very broad main lobe, resulting in poor frequency resolution.