Who says the poorest do? Is this a worldwide average, or a nationwide average, or a "poor/rich people I know" average...?
Surely it depends on the individual, and their personal generosity, or rather views on dishing out. Considering the amount some
extremely wealthy individuals give, if there's any sort of average being done with the "rich 'uns" and "poor 'uns" groups in mind (whatever they are...) then such donations running into the billions must ballance things out? Then you have to factor in the very wealthy, or even the moderately wealthy who aren't obsessing about their income, and merely give because they want to... maybe anonymously, maybe not.
Likewise, with the "poor", there are people giving anonymously, people donating a substantial portion of their income to causes etc etc. I assume this is what you view as relevant; the percentage of income received which is being given to help others. But then... you have to factor in a whole lot more complexities. Maybe the uber-super-rich off in their own world aren't so aware of groups and charities helping others... then again,maybe not, but it seems a bit of a jump to move to the "they're rich cos they're greedy cunts" mentality, or worthy of blame cos of supposed lack of generosity.
What about if.... effectiveness of donation, vs generosity of donation is weighed up? Some rich people might be giving huge sums which are wasted, and some poor might be giving smaller amounts which help enormously in day-to-day small projects. If you presume both have good intentions, is the rich-y better still, cos they've given "more"? Or you can flip reverse it, and say no matter if a poor person is giving a hugely generous proportion of what they earn, if most of it is getting lost along the way, taxed, caught up in bureaucracy, does it compare to an extremely wealthy person giving a fairly small amount, but distributed more effectively thus making a bigger difference.
Really, it's impossible to ever come to a realistic answer in many of these cases. To me, the virtues of charity are pretty hard to suss; everyone has different reasons really. Whether the effectiveness of donation, amount given or intention of giving take priority however, in solving some overall "pattern" of rich vs. poor is another matter, and in the end is inevitably gona be built upon stereotypes and generalisations. Very feel good...
Apologies for the ramble!