When you're spiking like that, I would suggest running [Adam Machanic's sp_whoIsActive][1] as a start to see if anything else is running that is taking up those resources.
But if it is just the one process, I would then start with @TRAD's idea of checking out statistics and indexes. 3GB of RAM isn't very much, but it's not totally inadequate, either, depending upon the circumstances--we comfortably run certain instances with less RAM than that. And based on how it's doing the inserts and reads, a nice index or two (depending upon the complexity of your query) might turn a lot of table scans into index seeks, which reduces resource requirements as well.
[1]: http://sqlblog.com/blogs/adam_machanic/archive/2011/04/27/who-is-active-v11-00-a-month-of-activity-monitoring-part-27-of-30.aspx
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