How do I set the default size for a stamp?

No disrespect to Thom Parker but Adobe Acrobat is lacking and I am not one of these other users. Sizing an image prior to making a stamp can be done but getting this correct is not at all straightforward. If you look at built in tools, just about every other object can be resized in acrobat via a dialog box. I don't see why adobe makes this more difficult on the user when Acrobat could have the ability to change the size of the stamp by "percent of size" in the properties dialog and then allow to set the "Default size" OR resize the object in acrobat and then allow it to be set as the Default size. I sholdn't have to mess around with it external to acrobat. Acrobat has such precision in most areas. Why not this?

Sounds like many others have the same problem. That's a clue to Adobe to look at it.

Change resolution in image with stamp to 400 pixels/inch and save tiff with transparent layer. 

The "workaround" you provided is the standard way of resizing and positioning an Acrobat Stamp.

Glad you figured out how to use Acrobat.

This is covered in Adobe's online HELP section: https://helpx.adobe.com/acrobat/using/adding-stamp-pdf.html (Scroll to the section "Change a stamp’s location or appearance"). And most likely there are probably a bazillion YouTube videos on it, too. And Help also has a section on how to create a basic stamp: https://helpx.adobe.com/acrobat/using/adding-stamp-pdf.html#create_a_custom_stamp.  Wooo Hooo!

Note that this is a user-to-user forum. None of us are Adobe employees, nor are we paid to be here. The ACPs and MVPs that answer questions are volunteering their knowledge to help other users. Occassionally an Adobe employee chimes in and you can see the red Adobe icon next to their name.

But we're not here to teach anyone how to use their software, nor give a private tutorial on doing this and that. So an answer like "The best solution for a correctly sized stamp is to create it in the correct size in the first place" is the single most accurate answer in this thread.

If you don't know how to size your original graphic in whatever software program you originally used, then don't shoot the messenger. It's your responsibility to learn how to do that. This is an Adobe Acrobat user forum; we have no idea what program you used to create the original graphic, and we can't cover the use of other programs.

Bottom line:

Get training in how to use Acrobat and its more advanced features. There are many options, some are free:

• Use Adobe's online help section at https://helpx.adobe.com/support/acrobat-b.html
• Use Adobe's free online tutorials at the same URL.
• Take a class from an online training center, like LinkedIn Learning. They have a deal giving you one month's free access to their entire library, so you can learn a lot in 30 days.
• Take a formal class from an Adobe Authorized Training Center or individual Certified Instructor (many are ACPs on this forum).  https://learning.adobe.com/partner-finder.html  Because they are Adobe certified, they teach the correct way to use Adobe's software programs.
• Search YouTube for short tutorials on the topic. Caution: like everything else on the web, you might not get accurate or current instructions. Unless you already know the correct methods, you can't tell if a YouTube video is giving you good advice or not. There's a lot of crap out there!
• Get a book! (Yes, I know this is a novel idea.)  Best for this topic: Adobe's Classroom-in-a-Book for Acrobat DC https://www.amazon.com/Adobe-Acrobat-DC-Classroom-Book/dp/0134171837 Available in print and digital formats. This is the official book on Acrobat that is used for training before becoming certified.

You need to resize the stamp file Acrobat created, or resize the image you used and then create a new stamp from it.