DIA has ~$35.62 billion, IYY has ~$2.5B in the DJIA. There are only 30 companies in it (~$12T total value), so it averages $1.1B per company.
But the S&P 500 index funds has somewhere around ~$2.5T invested, but that is spread across 500 companies (~$40T total valuation), so it averages $5B per company.
Thus you are correct the S&P 500 is more influential in terms of index fund reallocations, but only roughly 5x more influential.
The S&P 500 is cap-weighted, so the average value per company is meaningless. Nvidia is currently 7% of the index, while the smallest member is 0.01%.
Since Nvidia was already a part of the S&P 500 (and other similar indices) prior to its big run, those index investors generally profited from its rise. New flows into those funds do help prop it up, though.
The DJIA is a weird historical relic, and there's little reason for anyone to buy a fund tracking it. It's possible that those who did anyways will end up holding a tiny fraction of the bag due to this change, but it's not a big effect.
The dow has nothing to do with index funds. The dow industrial average is price weighted. The s&p 500 is market weighted. No competent index would follow the dow- it doesn't even make sense conceptually, it has zero relation to the economics of the companies when you use price weighting, and 30 companies is a stupid low number.
There is, as far as I can tell, zero point to the dow, it's a completely useless tracker that is reported on because people talk about it because it's reported on.
This may make sense in theory but in reality is wrong. The DJIA has historically had a very close correlation to the S&P. Plus there is an inescapable psychological aspect to the Dow that is unique. When the Dow is off 1500 points it hits much differently than the S&P falling 200 points.
I have a feeling that is because every company in the DJIA is also in S&P, and most are very heavily weighted in S&P. Rather then companies within the DJIA doing as good as companies in the S&P.
But the S&P 500 index funds has somewhere around ~$2.5T invested, but that is spread across 500 companies (~$40T total valuation), so it averages $5B per company.
Thus you are correct the S&P 500 is more influential in terms of index fund reallocations, but only roughly 5x more influential.