What type of soap making process did you use? What's your recipe? How long did you cure your bars?
Soap from the store may be wildly different in feel than homemade soap depending on what ingredients you used and what ingredients are in the store bought version. Many of store-bought soaps aren't even soap at all, but rather made from synthetic detergents (syndat bars, they are called) instead of being saponified oils.
The dimensions have nothing to do with it. The difference is the ingredients -- whether it's "syndets" as @MellonFriend mentioned, or actual "soap" made from the same ingredients we use to make handcrafted soap, or a combination of the two with tallow added to allow the manufacturer to call it soap!!! LOL
The other BIG difference is that commercial soaps are made in a factory with big machines that mix the ingredients, push the batch through an extruder that turns the soap into noodles that are then pressed into molds. (Simple explanation)
YouTube has videos of how Dove and Lux are manufactured if you want to have a look at the process. If you ever want to go BIG TIME, you can buy machines to simulate that process.
Those are all good questions. For one thing, "The longer the cure, the better the bar." So, if your soap is fairly new, it won't be as dense as when it is fully cured.
Your choice of FAs (Fatty Acids), additives and other ingredients also contribute to the density of the soap. Personally, I find that a simple, fully-cured,Basic Trinity of Oils bar comes the closest to the density and performance of commercial soaps.
Interesting! So the one I was looking at is handmade soap made with saponified oils. I was using cold process and used olive oil, coconut oil, palm oil, shea butter and sweet almond oil but the one I saw in store only used the first 3. Right now, one of my bars freshly cut weighs about 4.05 oz.
I see that combo all over the internet when a customer asks me to duplicate their favorite soap when it's no longer available -- Dr Squatch, Trader Joes, Green Mountain Vegetable Soap, etc. It's obviously a good seller!
Mass produced commercial soaps are made using industrial methods and highly refined ingredients.
One step in the commercial process uses high pressure to compress the finished product into industrial moulds directly, or through an extruder for cutting.
These commercial processes and ingredients combine to make soaps that are hard and dense from the day they are made.