This is my 3rd year growing garlics and still learning.
From what I have read here on GW, you shoul always plant the larger cloves, and use the inner small cloves for cooking. Small cloves will produce smaller garlics and might even produce a round single clove garlic.
But other than the seeds, certain growing conditions and care can make a difference in garlic size. Also the variety is another factor.
So, here I am. I also want to know how to grow bigger garlics.

The best advice I can give is that you browse the many pages of information in this forum. There are many experienced growers who contribute here. (Repeating everything umpty-jillion times gets old.)

The most important growth period for garlic is between the time it pops up in spring and the summer solstice. This time period gets shorter and shorter the farther north that one grows garlic. You want the garlic to grow as many leaves as possible during this period. The more leaves, the larger the bulb. Good compost, adequate water, and regular feedings of nitrogen (urea) are generally required to get decent-sized garlic in the north.

Variety makes such a huge diff in bulb size, and bigger ain't always better. The smallish bulbs of my Korean and Appalachian strains keep way better than the bigger bulbs of Music and Spanish Roja. The first year I grew the Korean I thought, what pitiful little things, but the bulbs are still perfect for eating (April), which is saying a lot.

I "band" organic fertilizer beneath the rows before planting in the fall, mulch through winter, and that's it.

I use a foliar spray of fish and seaweed emulsion about every 2-3 weeks during the growing season. I also spread chicken litter from the hen house cleaning between and next to the garlic bulbs as soon as I can in the spring. I assume that this is why my garlic and onions do so well.
luke