It's a unit of account (for the IMF and other international bodies') purposes. As well as just a basket of the most liquid and transferable currencies that reserve managers will all hold anyway in their normal course of business. It doesn't "move" FX markets.
The measures as I understand them are:
= basic liquidity and transferability (which is why there are only 4/5 in the basket in the first place).
- a country's IMF "quota", ie a country's shareholding in the IMF
- a country's trade intensity (ie their currency matters from a global trade perspective)
- a currency's intensity in global capital flows.
The last two reflecting the likelihood that economic changes could generate global capital and FX shifts that would cause FX reserve managers to shift reserve allocations. But the weights themselves are fixed for the 5 year rolling review period, so the SDR doesn't "mark-to-market" in a crisis. The idea is that the currencies included are those with the least chance of an Emerging Market-style currency crisis in the first place!
I'm not sure the precise scorecard is published in full; but its basic purpose is a unit of account rather than a trading instrument. And any counterparty of the IMF who wished to trade it with them, could and does trade exactly what they wanted in real time with the banks, exactly how they wanted, rather than through the SDR basket.