To investigate the formation and evolution of vertical structures in disk galaxies, we measure global $\operatorname{sech}^2$ scale heights, averaging thin and thick components when present, for 2631 edge-on disk galaxies with $M_*>10^{10} M_\odot$ at $0<z<3.5$ from the JWST COSMOS-Web survey. We show that dust extinction systematically overestimates scale heights at shorter rest-frame wavelengths, and therefore adopt a fixed rest-frame wavelength of 1 $μ$m. After further correcting for projection-induced bias using a new accurate method, we find that the median disk scale height increases from $0.56\pm0.03$ kpc at $z=3.25$ to $0.84\pm0.04$ kpc at $z=1.25$, and subsequently decreases to $0.67\pm0.06$ kpc at $z=0.25$. The bias-corrected disk scale-length-to-height ratio remains constant at $2.7\pm0.2$ for $z>1.5$, but rises to $4.0\pm0.4$ at $z=0.25$. These results imply that the high-redshift progenitors of present-day thick disks were of intermediate thickness, neither thin nor thick, yet dynamically hot and dense. The observed radial variation of scale height is consistent with the artificial flaring expected from observational effects, disfavoring minor mergers as the primary mechanism of disk thickening. Instead, we suggest that the high-redshift intermediate-thickness disks were single-component systems that increased their vertical scale height through decreasing surface mass density and/or violent gravitational instabilities, eventually producing thick disks. Thin-disk growth begins at $z\approx2$ and dominates at $z\lesssim1$, yielding a vertically more compact system with decreasing scale heights from $z\approx1$ to $0$. The inferred thin-disk mass fraction increases from $0.1\pm0.03$ at $z=1$ to $0.6\pm0.1$ at $z=0$. Together, these findings reveal a continuous evolutionary link between high-redshift single-component disks and present-day thick thin disk systems.

Recent analysis of 2968 MaNGA early type galaxies has yielded two notable trends with velocity dispersion ($σ$) not previously discussed in the literature. First, Fe abundance rises with $σ$, but only until $σ\approx100$ km s$^{-1}$, after which it falls. This kink is reproduced by TNG100 simulations, implying that hierarchical merger processes might explain it. Second, astrophysical scatter in N is high for galaxies with $σ< 100$ km s$^{-1}$. Due to the restricted list of nucleosynthetic sources for N, it is likely that asymptotic giant branch stars provide most of this N. A varied star formation history (compared to that of massive galaxies) along with variable retention and recycling of N-enriched gas might explain the fuzz of N abundance in low-$σ$ galaxies. Because a timescale argument seems necessary to explain the nitrogen fuzz, and an initial mass function argument is ruled out, similar timescale arguments for the [Mg/Fe] trend as a function of velocity dispersion are supported.