How can delta (Δ) R² for a term be larger than R² for that term? I am testing whether a variable predicts an outcome - firstly on its own, and then after controlling for various covariates. Since the outcome is continuous, I want to report R² as an effect size metric.
For that, I was planning to report

*

*R² for the DV ~ IV model, and

*ΔR² comparing DV ~ IV + CV minus DV ~ CV.

In some instances, the resulting ΔR² is larger than the corresponding R² - which does not seem to be possible with my understanding of what R2 indicates. How can a variable explain a greater incremental than total share of variance? I'd be very grateful for any pointers.

First, to get this nitpick out of the way: you are not predicting, you are fitting and explaining variance. These two are very much not the same. One model might explain much more variance (and even have a higher adjusted $R^2$) but yield worse predictions than a different model. In-sample fit is a notoriously bad guide to out-of-sample predictive power. Analyzing model fit and calling it "prediction" confuses two very different things, and every time I see a psych paper discussing "prediction", I am sorely tempted to ask them to actually do predict something and compare these predictions to a much simpler model on a true holdout sample. They would usually be shocked how little their statistically significant findings actually improve predictive power.

Now, this is just a situation where your intuition (that a variable should not explain more variance in the presence of a covariate than without that covariate) is off. There is simply no reason for this to be true.
You can simulate simple cases like this multiple times, playing around with your simulation parameters, and check whether the property your intuition calls for holds. Here is a simple case with $n=20$ data points, a numerical IV and a two-level factor CV where it doesn't:

Regressing DV on IV alone gives $R^2=0.01628121$. A model with DV and CV gives $R^2=0.4843284$, and one with only CV gives $R^2=0.4656828$, so
$$\Delta R^2 = 0.4656828-0.4843284 = 0.01864566, $$
larger than the single-predictor $R^2$.
Note that we are analyzing a correctly specified model with the two main effects. You could probably create more counterexamples with misspecification. In this case, the issue is that CV already explains a lot of variance, so when we regress only on the IV, we incorrectly believe we can explain some variance that is actually driven by CV - and in comparing the two competing models, this variance is correctly already explained by CV.
R code:
nn <- 20
set.seed(1)
IV <- runif(nn)
CV <- as.factor(rep(c("A","B"),each=nn/2))
DV <- 1*IV+2*as.numeric(CV)-0.0*IV*as.numeric(CV)+rnorm(nn,0,1)

plot(IV,DV,col=CV,pch=19+as.numeric(CV),las=1)

summary(lm(DV~IV))$r.squared
summary(lm(DV~IV+CV))$r.squared
summary(lm(DV~CV))$r.squared
summary(lm(DV~IV+CV))$r.squared-summary(lm(DV~CV))$r.squared

