Hide Page Title with Post Meta

$value is always empty because post ID is missing. Pass the parameter ($post object) to the hide_title_callback() function and get the post ID right way.

Also, you should take care of nonces.

<?php
// pass the $post object
function hide_title_callback( $post ) {

    // you have to verify this nonce inside `mysite_save_postdata()`
    // https://codex.wordpress.org/Function_Reference/wp_nonce_field
    wp_nonce_field( 'mysite_action_name', 'mysite_nonce_field_name' );

    // now you have the post ID
    $value = get_post_meta( $post->ID, '_mysite_meta_hide_title', true );

    if( $value == "on" ) : ?>
        <label for="hide">Hide: </label><input type="checkbox" name="hide" checked>
    <?php else : ?>
        <label for="hide">Hide: </label><input type="checkbox" name="hide">
    <?php endif;
}

Verify the nonce

<?php
function mysite_save_postdata( $post_id ) {
    // https://codex.wordpress.org/Function_Reference/wp_verify_nonce
    if ( !wp_verify_nonce( $_POST['mysite_nonce_field_name'], 'mysite_action_name' ) ) {
        return;
    }

    if ( isset( $_POST['hide']) ) {
        update_post_meta(
            $post_id,
            '_mysite_meta_hide_title',
            sanitize_text_field( $_POST['hide'] )
        );
    } else {
        update_post_meta(
            $post_id,
            '_mysite_meta_hide_title',
            sanitize_text_field( "off" )
        );
    }
}

To keep the database a bit cleaner I personally should not save the ‘off’ meta value. I should remove the _mysite_meta_hide_title completely if checkbox is unchecked. So, it will exist if ‘on’ and do not if ‘off’. if() statement in the hide_title_callback() will remain intact.

<?php
if ( ! isset( $_POST['hide'] ) ) {
    // unchecked
    delete_post_meta(
        $post_id,
        '_mysite_meta_hide_title',
    );
} else {
    // checked
    update_post_meta(
        $post_id,
        '_mysite_meta_hide_title',
        'on' // nothing to sanitize here
    );
}