Twitter error code 429 with Tweepy

You found the correct information about error code. In fact, the 429 code is returned when a request cannot be served due to the application’s rate limit having been exhausted for the resource.(from documentation)
I suppose that your problem regards not the quantity of data but the frequency.

Check the Twitter API rate limits (that are the same for tweepy).

Rate limits are divided into 15 minute intervals. All endpoints require authentication, so there is no concept of unauthenticated calls and rate limits. There are two initial buckets available for GET requests: 15 calls every 15 minutes, and 180 calls every 15 minutes.

I think that you can try to use API in this range to avoid the problem

Update
For the latest versions of Tweepy (from 3.2.0), the *wait_on_rate_limit * has been introduced.
If set to True, it allows to automatically avoid this problem.

From documentation:

wait_on_rate_limit – Whether or not to automatically wait for rate limits to replenish

Add wait_on_rate_limit=True on the API call like this:

api = tweepy.API(auth, wait_on_rate_limit=True)

This will make the rest of the code obey the rate limit

api =tweepy.API(auth,wait_on_rate_limit=True,wait_on_rate_limit_notify=True)

this should help for setting rate