You can use webfonts for your shop text. Probably the easiest to use are Google Web Fonts.
Paste the code needed to load the fonts into shop window > user fonts > font head code and the list of font-family names into shop window > user fonts > font family
Remember, you must also put the code to load the fonts into your shop site if it is not already there, or enable the font you require using your website builder settings. Tweak cannot do this for you as it only creates CSS.
With Google Web Fonts, the code and font families are shown in steps 3 and 4 of the "use" dialogue.
Here is an example using the Questrial and Josefin Sans fonts.http://www.ianholden.com/images/uservoice/tweak/fonts/fonts.jpg
Each font-family should be on a separate line and they will be listed in any font family drop-down selector in the tweak dialogs.
Now you have told Tweak about the fonts you wish to use, they should appear in all font selection drop-downs.
Tweak does not directly support changing fonts on all Ecwid elements, only the main ones, but you can use custom CSS to set other elements too. See How to change fonts for unsupported elements.