The size of a standard toolbar button is a user setting in ArcMap. If you want something larger than that then you can create your own custom toolbar control by implementing ICommand and IToolbarControl and creating a UserControl using the standard Form button. I don't use add-ins so I'm not sure if there is an add-in equivalent to that.
Yes you can set a button to text only on the toolbar, use the ICommandItem.style property. However, this is not really the original question. You can switch arcmap to display all the buttons bigger in Customize\customize mode under options tab, but the images are still 16X16 so they just look coarser. Having 32x32 icons is long, long overdue... Unless you are willing to do what Neil suggested, you are kid of stuck.
If you are using text and not an image, why don't you change the display to show "Text Only"?
Go into "Customize" and right click the button. And select "Text Only" instead of Default Style. Then it will show the "Name" of the add-in which you can adjust right there.
There is probably a way to set that as the default when the tool is added, but I do not know how to do that.