Asset Cat uses Dropbox as a method for storing assets in the cloud.  Although Dropbox's storage is limited on the free account, there are methods of increasing your size limit without subscribing to a larger storage plan like Dropbox Plus.

Here are some ways of getting extra free storage:

• Complete the Dropbox getting started guide
• Refer your friends, family, and coworkers to Dropbox
• Contribute to the Dropbox Community forum

Each time you Refer a Friend you gain 500MB.
Completing the Getting Started guide you earn 250MB.

There are other ways to earn storage, these offers are usually time-limited and are promotional offers for other apps.
At the time of this post, there are currently no promotional offers though that may change and you can often find out by searching recent articles on Google.

To view your current storage details, you can view your plan Here.