There are several factors that can contribute to continuously varying traits, and we have to be careful not to conflate them. They are often divided into two broad categories, genetic factors and environmental factors, although there are often non-linear interactions between these.
On the genetic side, traits come in several flavors. The two state trait, where either you have it or you don't, is the classical Mendelian trait. Peas in a particualr population are white or green. If you have two alleles for green, or one for green and one for white, you make green peas. If you have no alleles that code for the green pigment, you make white peas. Next, as you described, are the three state genetic traits. Still all coded for at one locus, but dosage dependent, you end up with 0 or .5 or 1 full dose of the gene product. This is called incomplete dominance.
Then you get into additive multi-gene traits. Many different genetic loci have can affect human height, as an example. There was one gene, who's name I don't remember, that was recently shown to exhibit incomplete dominance in affecting human height. AA individuals are on average 5mm taller than the background population, Aa individuals are, on average, no different from the background population, and aa individuals are on average 5mm shorter than the mean of the population. But obviously height in humans varies by more than 1cm, so their must be other factors contributing. Some of these factors are genes affecting the length or shape of individual bones. Of those, some are classically dominant, some are incompletely dominant, and some may even be overdominant (where the Bb individual would have a longer bone than the BB or the bb). When you add together the variation in all these genes, you have a huge range of possible combinations, and end up with data that look pretty continuous. But then it gets even more complicated.
Genetic effects are not always additive. Imagine one gene codes for the presence a knob on a bone, and another gene causes that knob to be long or short. If an individual has the allele that causes that knob not to exist, it doesn't matter whether or not it has the allele that would make that knob long. If the knob isn't there, it can't be long. This is called epistasis. The sole effect of many genes, on a molecular level, is to regulate the activity of other genes. One gene makes a protein that carves up the protein product of a second gene, preventing that second protein from binding to a particular point on a chromosome where it would keep a third gene from being transcribed. Raise the temperature slightly, and the first protein changes conformation, and lets the second protein be, which cuts off production of the thrid gene. But if the Sodium concentration in the cell is too high, the third gene will be turned off anyway, because the excess sodium prevents the change in conformation of the first protein. People have mapped out enourmous cascades of gene effects with many branches, feedback loops, multiple environmental and epigentic modifiers and so forth. Just about every gene is pleiotropic, meaning that is has more than one effect. Similarly, almost every gene has multiple things that determine when, where, and how strongly it is expressed. Genes can also have synergistic interactions, competitive interactions, and so on.
So the genetics allow for a large number of possibilities, meaning that even purely genetic traits can vary close to continuously. But very few traits are purely genetic. Human height certainly isn't. The nutritional state of your mother before and during her pregnancy has an effect on your height. So does your own nutrition during the time you are growing. My grandfathers, who were cold and hungry through much of their childhoods, were shorter than any of their male grandchildren. My grandmothers, similarly, were shorter than any of their granddaughters. We, and our parents, ate better, so we grew more. Most Americans are taller than their grandparents were, not because of any genetic change, but because our environment is different than theirs was.
Once again, there are non-linear interactions, both between environmental effects, and between environment and genes. In some cases organisms seem to be genetically programmed to let the environment have a very strong effect on their development. I won't go into detail because I think you get the picture. We are vastly complex systems, and their is ample opportunity for feedback, interference, competition and so forth. And given the number of inputs, and the complexity of the algorithm, continuous outputs are nearly inevitable. Even classical Mendelian traits are rarely all that discrete in their distribution if one allows environment to vary and does not have an inbred population.
As for growth thresholds, what tells a bone to stop getting longer now, and start growing internally instead, I know very little. The molecular basis of development is a very active field of research, but is far enough from my own that I haven't paid much attention to it.
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