The 500 fund has sector weightings based on market cap. This one has equal weightings.
Is there any theory behind this sort of weighting or is just one of those things that someone figured was worth a shot?
Another way to think about it: market cap weighting is a momentum strategy. Equal across sectors is mean reversion.
In this case, the equal weighting is abstracted away by 1 layer - each ETF is already cap weighted, so you aren't getting the full effect of equal weighting. Instead, you're reallocating to the ETF that has underperformed relative to all others, so as already pointed out, you are betting on reversion rather than momentum.
Just because the sector is big doesn't mean the companies in that sector are big.
If the sector is big because it has a lot of medium/small sized constituents you gain from this implementation because a cap weighted index would under allocate to these smaller names.