Why does the GoBabyTrade web only buy a small number of shares even though my account has enough to buy a lot more?

It trades in smaller share/lot sizes so that it reserves enough funds to be able to continuously buy/sell when the price goes lower.

If you were to use up all of your funds on a single purchase, you would not have any reserve funds to buy/sell at lower prices.
This money-management is built into the web app.