Akeeba Backup is not just a component. It's a package which combines a component, a library and some plugins. You cannot install it by directly uploading it to your server. This has been the case with all non-trivial Joomla extensions since 2012.
The issue with the file being too big has to do with your PHP configuration. There is a warning about it in your Extensions, Manage, Warnings page with a link that has more information about it. You can ask your host how to make it so that the maximum upload size in PHP is at least 4MB. Or you could read something like https://www.joomforest.com/kb/known-issues/how-to-increase-php-upload-limit-for-joomla which explains how to do it yourself.
Alternatively, you can use the Install from URL feature to circumvent this limitation of your current PHP server settings.
First go to our Downloads page. Make sure you are logged into our site. In the Akeeba Backup area you will see an All Files link. Click on it to see all files available for download in the current version 7.3.2.1. Scroll down to the Akeeba Backup Professional installation package. There's a Direct Link link below it. Right click on it and choose Copy URL, Copy link or Copy depending on your browser. The Direct Link URL is special. It contains your Download ID, therefore allowing Joomla to download the file without being logged into our site (Joomla downloads files directly from your server; whether or not your browser, on your computer, is logged in or not is irrelevant: Joomla's downloads all appear to come from a guest which is not logged into our site).
Go to your site's administrator. Click on Extensions, Manage, Install. Click the Install from URL tab. Paste the Direct Link you copied from our site into the URL text box in the middle of the page. Now click the Install from URL button. Joomla will download Akeeba Backup Professional from our servers and install it on your site.
Nicholas K. Dionysopoulos
Lead Developer and Director
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