To use a particular shipping method based on order total weight

functions.php

add_filter( 'wf_rate_for_service', 'wf_force_rate_on_weight', 10, 2 );
function wf_force_rate_on_weight($rates, $packages){
	$weight_less_than[] 	= array('weight'=>1, 'service_code'=>'US-EMI', 'package_type'=>'USPS flat rate envelope'); //Enter proper values or remove this line
	$weight_greater_than[]	= array('weight'=>1, 'service_code'=>'US-EMI', 'package_type'=>'Package'); //Enter proper values or remove this line
	$weight_equal_to[]	= array('weight'=>1, 'service_code'=>'US-EMI', 'package_type'=>'USPS flat rate envelope'); //Enter proper values or remove this line

	$weight_less_than[] 	= array('weight'=>1, 'service_code'=>'US-XM', 'package_type'=>'USPS Legal Flat Rate Envelope'); //Enter proper values or remove this line
	$weight_greater_than[]	= array('weight'=>1, 'service_code'=>'US-XM', 'package_type'=>'Package'); //Enter proper values or remove this line
	$weight_equal_to[]	= array('weight'=>1, 'service_code'=>'US-XM', 'package_type'=>'USPS Legal Flat Rate Envelope'); //Enter proper values or remove this line

	//find total cart weight
	$total_weight = 0;
	foreach ($packages as $key => $package) {
		$total_weight += ( $package['request']['Rate']['WeightLb'] + ( $package['request']['Rate']['WeightOz'] ) / 10 ) * $package['quantity'];
	}

	//process less than
	foreach ($weight_less_than as $key => $value) {
		if( $total_weight < $value['weight'] ){
			//if the given package_type is available for given service.
			if( isset( $rates[ $value['service_code'] ] ) && array_key_exists( $value['package_type'], $rates[ $value['service_code'] ] ) ){
				foreach ( $rates[ $value['service_code'] ] as $package_type => $package_type_value ) {
					if( $package_type != $value['package_type'] ){
						unset( $rates[ $value['service_code'] ][$package_type] );
					}
				}
			}
		}
	}

	//process greater than
	foreach ($weight_greater_than as $key => $value) {
		if( $total_weight > $value['weight'] ){
			//if the given package_type is available for given service.
			if( isset( $rates[ $value['service_code'] ] ) && array_key_exists( $value['package_type'], $rates[ $value['service_code'] ] ) ){
				foreach ( $rates[ $value['service_code'] ] as $package_type => $package_type_value ) {
					if( $package_type != $value['package_type'] ){
						unset( $rates[ $value['service_code'] ][$package_type] );
					}
				}
			}
		}
	}

	//process eaqual to
	foreach ($weight_equal_to as $key => $value) {
		if( $total_weight = $value['weight'] ){
			//if the given package_type is available for given service.
			if( isset( $rates[ $value['service_code'] ] ) && array_key_exists( $value['package_type'], $rates[ $value['service_code'] ] ) ){
				foreach ( $rates[ $value['service_code'] ] as $package_type => $package_type_value ) {
					if( $package_type != $value['package_type'] ){
						unset( $rates[ $value['service_code'] ][$package_type] );
					}
				}
			}
		}
	}
	return $rates;
}