Mailstore Home is light nor heavy and looks likely too fancy when you start using it. However, it can import all your .eml messages (and attachments!), from which it creates a database that allows you to search quickly through messages and attachments. Once imported you can view the selected message as they are intended. Copy-paste info, attachments etc.
It is freeware and also available as a PortableApp (but you must have the correct .NET version installed in Windows), if that is your thing. Anyway, searches are fast with more search options than I have seen in any mail client, it can even act as a "mail client", but only for receiving messages from an account on a mail server. Myself, I use it for keeping a mail archive spanning over ten years. Most days I receive over more than 100 messages, often with one or more attachments. Searches still only take a few seconds.
Once you have set it up as you like it, you will quickly wonder how you ever managed without it. No other association than being a happy user.