To get big onions you have to have the right type and variety. Everything else is secondary.

Onions are short, long or intermediate day. This designation determines when they begin forming the bulb. Get the wrong type and the bulb forms at an inopportune time and doesn't get big. I suspect you are a long day grower as I am, but check on a map to be sure. Here is one. Scroll half way down the page.

Next is the variety. Some, due to genetics will get larger than others under the same conditions. It helps to know what you are buying versus getting unnamed varieties in a store. I have commonly seen onions for sale locally that are short day varieties when only long day will do well here.

As far as your soil, don't worry about that yet. Obviously loosen it up and enrich it with any organic matter and you do a good thing, but first get the type and variety right. If you read the FAQ at the link I gave you it contains a lot of useful growing information.

I, and others here, get onion plants from them every year.

June 1st is too late to plant onions if you expect them to get any size. April is more like it. Or as soon as the ground can be worked. They are day length sensitive and will stop growing when the days start to get shorter.
Sets won't give as big onions as plant but sets will get to a very satisfactory size and are easier to handle. Plant them 6" apart in soil enriched with compost and when they start growing, side-dress with a complete fertilizer )5-10-5 or 10-10-10. And make sure they get enough water in June and July. By August the tops should start to die down and you can harvest them as soon as most of the tops are dry.

didn't notice the plant out date you gave. I agree 100% with old roser that June is waaaay too late in your zone. I plant April 15th and I am one zone colder than you. Plant onions well before your last frost date. They are not frost sensitive plants so they can go out as soon as the snow melts and the ground thaws.

Old Roser is also quite right about watering in the hot months, onions like lots of food and water.

Still, make sure you get varieties that are the right day length for your area or all is for naught.

ONe of the most important things in growing big onions is to plant them out real early. Hard to have nice workable soil most springs in Ohio so I use this method.
In the fall I till deeply where the onions are going to be in the spring. I till as much rotted leaves in as the ground can take. Then I rake long hills, pulling soil from both sides of hills. Leaving room to walk between hills. During the winter the ground will be frozen and thawed to break down the clods. Come spring these hills will be the first ground to dry out. If I see rain coming about the time to plant the onions, I will cover the hills with plastic. I aim for the first week of April for onion plants. When ready to plant, I knock the hills down with a tiller so that it is about 4 inches tall and 20 plus inches wide. I plant two rows of plants 1 foot apart.At least 6 inches between plants in rows. I then mulch with rotted leaves, make sure to never let them go without water for very long and keep the few weeds out that sneak up through the leaves. Works for me and I ain't going to change until something better comes along. Candy onions get huge with this method for me, anyhow.Where I plant onions the soil is clay type, but years of leaf mold has turned the soil blackish. I am going to try planting in a sandy loam that I have in raised beds this year and see if the oinions get bigger yet.Even if I had sandy loam on flat ground, I would still make hills in the fall so I could plant even earlier in the spring. Geezer

Thank You all, Username 5 for the wealth of information, Oldroser for catching my fatal flaw and Geezer66 for explaining how to work my cold icy soil! I couldn't put all the pieces together but now I get it. I'm going to take pictures of this year crop and next year I will post them to show other newbies the difference. Maggie

Variety is (almost) everything if you want size. I grew Greek Salad for red and Varsity for white spanish type. I got both from Fedco seeds of Maine.
Both were excellent healthy growers that produced softball size onions. they kept well - until April! and I planted them again this year. I pull them up when the tops start to dry off and flop over.

All onions seem to like rich un-compacted soil.

Good luck!
Maryanne in WMass

I was reading that onions are bieneial, does that mean I have to wait for the second year to get bulbs. I just started some seed indoors the other day with the hopes that if i planted out in the spring, by fall I would have a nice harvest. First year to try growing onions.

Onions are biennial in that it's the second year that they bloom. The first year, they spend all of their time storing up energy for the second year. Thus you will indeed get bulbs the first year, assuming that you are planting a bulbing type.

Martin