The size of the SD card has no bearing on downloaded apps, unless the phone is 1. running Android "Marshmallow" and 2. you have the card set up as "Internal" storage. If these were not done, then the items will be only trying to download directly to the phone. Below are the instructions on how to make a card "Internal" rather than "External" storage. But please note, not all phones can do this. If you don't have the right version of Android, or the manufacturer has restricted the option, then it won't work.
How to turn external SD card into internal storage on "Marshmallow".
NOTE: Please be sure you start with a blank SD card. It needs to be blank because when the card is converted to "Internal" storage, it will be formatted (wiped) and encoded (making the cards data only readable by that device).
1. Go to device “Settings”, then select “Storage”.
2. Select your "SD Card", then tap the “three-dot menu“ (top-right), now select “Settings” from in there.
3. Now select “Format as internal”, and then “Erase & Format”.
4. Your SD Card will now be formatted as internal storage.
5. Reboot your phone.
NOTE: If you don't reboot the phone, many things may not work correctly, so make sure you do.