What are some alternatives?
When comparing TortoiseGit and Gitweb, you can also consider the following products
GitKraken - The intuitive, fast, and beautiful cross-platform Git client.
GitLab - Create, review and deploy code together with GitLab open source git repo management software | GitLab
SmartGit - SmartGit is a front-end for the distributed version control system Git and runs on Windows, Mac OS...
GitHub - Originally founded as a project to simplify sharing code, GitHub has grown into an application used by over a million people to store over two million code repositories, making GitHub the largest code host in the world.
SourceTree - Mac and Windows client for Mercurial and Git.
GitHub Desktop - GitHub Desktop is a seamless way to contribute to projects on GitHub and GitHub Enterprise.