I can really comment only on those that I know:

Heavy
Squashes
cucumber
eggplant

Medium
Beans

Light
peas
turnips

As for the nutrients and minerals, well, that's quite a list. Some are known as micro-nutrients insofar as they are required in such small quantities. These include things like boron, manganese, cadmium, zinc etc. One of the best ways to deliver all of these in one application is either kelp meal or glacial sand.

Then there are the essentials like iron, calcium and magnesium. These are probably the big three that most gardeners will have to worry about. Iron is a problem because there are very few additives that will provide iron in a readily available format. My grandfather used to put iron spikes/nails into the soil, but it's hard to know if this actually worked. As far as the calcium and magnesium, dolomitic lime takes care of those.

Then the biggies: nitrogen, phosphorus, and potassium. These are the standard NPK that you see referenced in almost every fertilizer. Too much of any of them will lead to balance problems, so you best off with a balanced, slow release fertilizer. You can get the same results with chemical fertilizers (despite what hardcore organic gardeners will tell you), but they are very difficult to use successfully because they are so powerful. Also, long term soil health can be easily harmed by chemical fertilizers (same applies to the "organic" fertilizers too, it just takes longer to destroy the soil).

Beyond these, I wouldn't worry about it too much because you will have difficulty controlling micro-nutrient levels. Factors like soil type, irrigation, heat, organic matter levels, etc. all have an effect on both the presence of the nutrients and their availability.

It may sound a bit simple but compost tea or a worm compost tea as a foliar spray or side dressing should give the plants all or nearly all of the macro and micro nutrients they need--unless there is a soil nutrient deficiency which could be mostly solved with a sidedressing of aged compost over a year or two's time.

Here is a link that might be useful: HarvestToTable.com

I don't know that I agree with the original list to start with. Light feeders of what? Nitrogen? Then all pulses are the lightest feeders, but also most root crops (except potatoes) will grow well in soil that was manured the year before (but not this year).

Potassium? Then the fruiting plants typically use a lot. The K in a melon or a tomato, which is more than the K in a banana, comes from somewhere. But tomatoes don't need extra N particularly, there are many greens (say, broccoli or cabbage) which need more N.

Phosphorus? Most people over-fertilize with P, given that the fertilizer one buys is 10/10/10 instead of 8/2/6 or close to these ratios.

If I'm not mistaken, the list comes from Steve Solomon (or at least Solomon has a similar list, using Low-Demand, Medium-Demand, High-Demand). His point is that low-demand plants should be able to grow reasonably well in soil that has either no or minimal inputs. As you move up the list to the higher demanding plants, you are going to require supplemental fertilizer (be it N, P, or K, or all three) to fully develop the plants to their full potential.

Not rocket-science or ground-breaking, but he is writing in the context of quasi-survival gardening where inputs may not be available (scarcity or economics).

When I was asking which vegetables are considered heavy feeders, which are considered moderate feeders, and which are
considered light feeders it was a very general and basic question.

Allow me to elaborate on that. When I was asking this question about fertilizing vegetables, I wasn't asking which are considered a heavy, moderate, and light feeder with a particular nutrient/mineral that any given vegetable needs to thrive and grow. When I asked which vegetables are considered heavy feeders, which are considered moderate feeders, and which are considered light feeders what I wanted to know is which need heavy amounts of fertilization, which require moderate amounts of fertilization, and which require light amounts of fertilization sparingly.

I managed to acquire some information on the six main nutrients any plant needs to grow and thrive. These apparently are known as macro nutrients and they are:

nitrogen
phosphorous
potassium
calcium
magnesium
sulfur

I have also heard that veggies or any other plant for that matter need what are called micronutrients, which are nutrients they need as well, but in much smaller amounts.

Basically I have two questions.

One, with the list of veggies I have given, what veggies need large and sufficient amounts of which macronutrients.
Two, what is a list of common micro nutrients.

The reason I'm asking for this information is because I know that if a vegetable doesn't get adequate sources of the macro nutrients it needs to grow and thrive, then it will die. If it doesn't die due to lack of nutrients that it requires, then it will be very sick and weak, which quite frankly isn't much better.

I don't know which of the different veggies need different amounts of each of the major nutrients. The whole reason I posted here was to request that information and to acquire it because I don't know and I need to know this information.

Answer to the concern of a sick and weak garden: make compost out of any and all organic material, including cardboard, leaves, and human urine in addition to kitchen waste. "make" is almost to strong a word when it comes to compost. Put it in a pile, put it in a trench in the garden, put it wherever and the nutrients will find their way to the microbes.