There is no particular meaning to AIC for comparison between different data sets. Yes, the AIC value can change for increased $n$. However, AIC is self-referential, which means that one can only compare different models using the SAME data set, not different data sets. This is also tricky, for example, it probably applies to nested models (models that are in a set/subset format, that is, when all of the models tested can be obtained by eliminating parameters from the most inclusive model).
Some experts suggest that AIC also applies to non-nested models, but there are counterexamples, see this Q/A. Perhaps a more meaningful question, that the OP question above is only indirectly implying, is "How well AIC can discriminate between two models when the sample is larger?" and the answer to that is apparently better for increasing $n$. This latter is not unexpected in the sense that AIC is only asymptotically correct, e.g., from Wikipedia, "We ... choose the candidate model that minimized the information loss. We cannot choose with certainty, because we do not know f (Sic, the unknown data generating process). Akaike (1974) showed, however, that we can estimate, via AIC, how much more (or less) information is lost by g1 than by g2. The estimate, though, is only valid asymptotically; if the number of data points is small, then some correction is often necessary (see AICc...)."