First we need to consider the Hawaiian Islands in their full context, i.e., the Hawaii-Emperor Seamount Chain, which are all generated from the same hotspot. To make sure we're all on the same page, yes, the general idea is that the hotspot is semi-fixed with respect to the moving plates (reality is a bit more ugly, e.g., this FAQ - but for our purposes we can say the hotspot is effectively fixed). As such there is hotspot volcanism in the location above the hotspot for a time - which if the hotspot is erupting through an oceanic section of a plate and magma production is sufficient, will tend to produce an island - until this spot on the plate is advected away sufficiently by plate motion to generate a new eruptive center, eventually forming a new island (again, reality is a bit more complicated in terms of how connection between a soon-to-be-dead and new eruptive centers are severed and established, again, covered in one of our FAQs). For kind of schematic representation, consider this image from the National Park Service.

For the Hawaii-Emperor chain, if we look along this full hotspot trend, we'll see a general pattern of increasing size and elevation going from the oldest end (i.e., the bit that is actively being subducted at the Kuril Trench) to the youngest end (i.e., the Hawaiian islands). The reasons for this progressive increase in size are three fold:

1. Subsidence. This is probably the largest effect, but the relative contribution between it and the next driver are a bit hard to partition out. In short, in addition to the volcanism, there are two things that are happening in the section of oceanic lithosphere directly above the plume, it's getting hotter AND it's physically being pushed up by the warmer, more buoyant section of the mantle that is the plume itself. For the first, generally warmer lithosphere is less dense and through isostasy tends to have higher average elevation (this, for example, is why depth of portions of the oceanic basins are largely tied to lithospheric age since for areas not influenced by a hotspot, age is a proxy for temperature as sections lose heat as they move away from mid-ocean ridges). For the second, the plume in the mantle generates a "swell", i.e., a dome like uplift centered on the plume, which would fall under the umbrella of dynamic topography. As an oceanic island is advected away from the plume, it will subside (i.e., sink) both through thermal relaxation (i.e., it and the surrounding lithosphere will get colder and more dense) and from moving off the swell under the plume. This means you generally expect oceanic islands to decrease in elevation and thus reduce in size at the surface (until they completely sink, becoming seamounts, guyots, etc.). Recent work would suggest of these two forces, subsidence related to moving off the swell is the dominant one (e.g., Huppert et al., 2020).
2. Magma supply. The productivity of a plume, both in terms of melt generated but also the amount of melt that successfully erupts and contributes to the volume of oceanic island in question, is not necessarily constant. In the case of the Hawaii-Emperor chain, considering its longterm magma supply rate (e.g., Figure 2 from Poland et al., 2014) suggests that broadly the time in which the modern Hawaiian chain was forming (e.g., the last ~5 million years) represents a period of heightened productivity. Specifically for the big island, we can see that some estimates (e.g., the Vidal and Bonneville one) suggest that the modern productivity is significantly higher than anytime in the past.
3. Erosion. While not a dominant factor generally (at least compared to either subsidence or supply), while an oceanic hotspot island is above the plume and actively erupting frequently, the topographic expression of the plume reflects a balance between material added via volcanism and material removed by erosion (along with the isostatic and dynamic effects discussed in point 1). Once the volcanic system is shut off, the edifice will be degraded by erosion with effectively no processes to balance it out. Erosion will come in the form of river and hillslope processes, wave action, and mass wasting. The last can be significant for oceanic hotspot islands as they are prone to large "mega-landslides" (e.g., Holcomb & Searle, 1991, Oehler et al., 2008, etc). The Hawaiian islands are no exception and in fact a significant portion of O'ahu broke off ~1 million years ago and is visible in the bathymetry (i.e., the Nuʻuanu Slide). Broadly, once an island has been submerged through the combined action of subsidence and erosion, most of the erosional processes will stop (whereas the subsidence processes will continue).

Taken together, even without the Hawaii-Emperor specific bit of a general trend in increasing eruption rates, with just the patterns in subsidence and erosion, you would broadly expect that the most recent main eruptive center within an oceanic hotspot track to usually be the largest. Adding in the trend toward greater eruptive volumes through time that we see in the Hawaii-Emperor chain further reinforces this pattern. However, we always have to consider that we're looking at snapshots of a dynamic system. For example, the big island is the youngest subaerial part of the Hawaii-Emperor system (and also the largest), but it's not the youngest part of the system as a whole. A new seamount (and likely eventually a new island) has been forming for the last ~400,000 years to the southeast of the big island, i.e., Kamaʻehuakanaloa. The subsequent evolution of the system, e.g., when will Kamaʻehuakanaloa eclipse the big island in terms of size, is hard to predict since projecting out the eruption rates and accounting for things like mega landslides are challenging.

[removed]

[removed]

[removed]

[removed]

[deleted]

[removed]

[removed]

[removed]

[removed]