Auto-add paragraphs to custom field?

Why don’t you use apply_filters( 'the_content', $var ); when outputting your custom field? You don’t really want to save the extra paragraphs, otherwise you’ll end up seeing them when editing the custom field. This is not what happens with WordPress.

If you’re not happy with what the_content does (it does a lot of things including wpautop) then create a custom filter like this:

// Assuming $var is your custom field value
add_filter( 'my_custom_filter', 'wpautop' );
echo apply_filters( 'my_custom_filter', $var );

Cheers!