Make the 'Weight' field required in WooCommerce Edit Product page.

add-required-attribute.js

jQuery(document).ready(function($){
	$('#_weight').prop('required',true);  // Set weight field as required.
});

set-focus-to-weight-field.js

jQuery(document).ready(function($){
	$( '#publish' ).on( 'click', function() {
		weight = $.trim($('#_weight').val());
		if ( weight == '' || weight == 0  ) {
			alert( 'Weight must be set in the Shipping tab.' );
			
			$( '.shipping_tab > a' ).click();  // Click on 'Shipping' tab.
			$( '#_weight' ).focus();  // Focus on Weight field.
			return false;
		}
	});
});

weight-required-field.php

<?php
/*
Plugin Name: Require Weight field (WooCommerce)
Plugin URI: https://www.damiencarbery.com/2018/01/make-weight-a-required-field-in-woocommerce/
Description: Require that the Weight field have a value.
Author: Damien Carbery
Author URI: http://www.damiencarbery.com
Version: 0.2
WC tested up to: 5.2.2
*/


add_action( 'admin_head', 'dcwd_require_weight_field' );
function dcwd_require_weight_field() {
	$screen         = get_current_screen();
	$screen_id      = $screen ? $screen->id : ''; 
	if ( $screen_id == 'product' ) {
?>
<script>
jQuery(document).ready(function($){
	$('#_weight').prop('required',true);  // Set weight field as required.

	$( '#publish' ).on( 'click', function() {
		weight = $.trim($('#_weight').val());
		if ( weight == '' || weight == 0  ) {
			alert( 'Weight must be set in the Shipping tab.' );
			
			$( '.shipping_tab > a' ).click();  // Click on 'Shipping' tab.
			$( '#_weight' ).focus();  // Focus on Weight field.
			return false;
		}
	});
});
</script>
<?php
	}
}