Is there any way to change the size of the browse dialog programmatically or at design time?

Yes, you can change it at design-time by opening up the FormLayoutSettings property (it shows the type editor form with the spitter bars and the 3 combo boxes where you can choose what shows up where).  Whatever size you leave the form when you click "OK", the form will be that size when it opens at runtime.

As for programmatically setting the size, you can adjust the FormLayoutSettings property on the browse dialog before you show it.