If you have setup your Gmail using Google Sync (as an Exchange account) then it is doable. If you'd like to do this follow these instructions:
Set up Google Sync with your iOS device
There are other benefits to this such as Exchange-like calendar pushing and proper push support for mail.
Then, go to the Settings app and under Mail, Contacts, Calendars select the account you want to limit the retrieval of mail for.
Underneath the sliders that enable the components of the account (e.g. contacts, calendars or mail) you will have the following option
- Mail Days to Sync
- Mail Folders to Push
The first of these is what you want. If set to 2 weeks then only the last 2 weeks of mail is synced with your phone.
I prefer however to have No Limit with this option and choose to limit which folders get synced (with the second option). If you keep a tidy inbox and archive mail to folders then this can be a sensible way forward.