The media upload size in WordPress/MediaPress are controlled by php.ini settings.
By default, the upload size of a media is limited by following php options:-
upload_max_filesize and post_max_size controls the maximum upload size while the max_execution_time decides when the script will be terminated.
If you want to increase the allowed size, we recommend changing these settings in the php.ini appropriately. If you make these changes in your global php.ini, please make sure to restart your web server( apache/nginx etc ).
upload_max_filesize = 80M
post_max_size = 85M
max_execution_time = 600
In the above, we allow uploading upto 80 MB (post_max_size should be slightly higher than the upload_max_filesize). Also, we have increased the script timeout to 10 minutes. Please do note that these settings will have effect on all parts of your site. Please choose carefully.