Lightweight browser recommendations?

[amyklai]

That T61 can take up to 8 GB of RAM.
Just upgrade the RAM, and reinstall Windows with the 64bit variant. And while your at it, swap the hard drive for an SSD. Both RAM and SSDs are pretty cheap these days and your Thinkpad will feel like a whole new notebook.

And you won't have to worry about which browser to run.

 

[coasthub]

I would say avoid Chrome if you are looking for a browser that doesn't eat up your memory fast. Chrome is very memory intensive even it's the fastest browser on the market (as Google says). Also avoid using IE based browsers like Avant Browser which is a clone of Internet Explorer with a different user interface.
Once you launch a the browser, bring up Task Manager and see how many processes it has and the total of the processes memory. As you open more tabs this number will increase or may even double.

Hope you've got an idea of where you'll be heading if you use the most popular browsers.