I am growing green onions from cuttings but have been dissatisfied with the outcome. My green onions are scrawny. Even when I've added some compost from decayed leaf cuttings, the green onions haven't reached the same size as grocery-bought ones. What can I do to make them grow larger?
How much sun are they getting? Onions need close to full sun in order to do really well. Onions are also considered moderately heavy feeders - this means that the compost you are using may not contain enough nitrogen to meet the needs of your onion starts. If you want to stay organic, there are plenty of granular or liquid organic fertilizers that are fine for food plants that you can try one to see if this boosts the growth of your plants.
Onions also are rather shallow-rooted and do not like, nor well tolerate, competition from weeds. If you have any weeds in the onion bed, you should remove them and keep them removed for the growing season.
Another question - what is the weather like now where you are? If it is very hot and dry, your onions will not grow well. If it is cold, they will grow more slowly. They like to make the majority of their green growth when the weather is cool-to-mildly-warm and moist but not soggy.
Edited to add: Oh, also, just to be sure - you are growing green salad onions, not chives, correct? I'm asking because green salad onions are generally not started "from cuttings" but chives are often divided and passed around as starts, which is kind of the same thing. If you indeed have chives, they will never get as big as grocery store green onions. They will, however, divide and live for a long time and in my opinion, taste just as nice.