I'll leave the question on if it's possible to install / run / maintain the PI Data Archive without AF and SQL to others to answer. It might be technically possible, but considering the effort potentially required to keep this unsupported configuration running fine over the next years i'd advise against it. Even for cost reasons.
If you're really pressed, you can safely install PI, AF and SQL on one host. Still not recommended, but in my opinion a better approach than not using AF at all.
SQLserver does not need to take a lot of memory. If you don't effectively use SQLserver, you can tune down the memory consumed considerably (e.g. using the "max server memory" setting). Google will be able to provide you with a plethora of answers to that question.
Hope this helps!
PI Server version 2010 (3.4.385.59) introduces PI Asset Framework (PI AF) as integrated part of the PI System. The latest release that does not require PI AF is 3.4.380.70 from July 2011.
PI Server 2012 requires a PI AF Server installation as prerequisite. Running PI Server (PI Data Archive) later than 3.4.380.70 without PI AF is not supported.
Please also keep in mind that even you do not use PI Asset Framework, there might be components requiring PI AF to store their configuration but I do not expect heavy resource usage because of this. As mentioned by Roger, without using PI AF you shouldn't expect heavy resource usage by it respectively by SQL Server.