Fixed Focus

All cameras need to be focused before shooting. There are 3 alternatives: manual focus, autofocus and fixed focus. The latter is an economical choice that can't work under all circumstances, it's OK only when the depth of field is large enough. This depth depends on the characteristics of the lens.
I can see a similarity in NMR spectroscopy. The phase correction of an high-resolution spectrum is like a lens with a limited depth of field (think to a telescope, if you are more familiar with them; the telescope is an example of a lens with a narrow depth of field). Starting from the optimal correction, a minimal change in the phase correction parameter (movement of the lens, in the parallel example) causes a visible negative effect on the spectrum (clearness of the image). It's not enough to copy the phase correction from a spectrum to the other, you must use either manual or automatic correction or both. Like it or not, you'll become an expert in the field.
Weighting is much more tolerant to a small change of the parameters, to the point that most of us use the "Fixed Focus" approach. We can even store the optimal value inside our standard parameters and forget about it. When you have forgotten it, it's arduous to improve your skill; DSP (digital signal processing) contains too much theory and practice is time consuming.
My rules are:

1. Weighting is an alteration of the spectrum. An altered spectrum may look ugly, don't worry.
2. It's more important to know what I want to obtain (where I want to go) that the way to go there, because many roads lead to the same place, but I must be able to recognize my destination if I arrive there.

While I usually recommend to observe and practice, because 50% of NMR can be deducted with common sense, there is a case where you need the theory, otherwise you go nowhere. If you keep weighting a standard COSY spectrum with the same functions that you use in 1D spectroscopy, you'll always get star-shaped peaks like this:
[after exponential weighting along both dimensions]

It's only theory that tells you that a symmetric FID corresponds to a symmetric spectrum, therefore if your weighted FID has a symmetric envelope, the dispersion component will be attenuated in frequency domain. In simpler words: use a sine-bell. It's counter-intuitive to zero the less noisy part of your spectrum, but look at the final effect:
[after weighting with two pure sine bells]