Why is the pricing of my GCP instance going down every week and comes back up at the beginning of each month?

The prices don't change, but an increasing discount is applied when your instances run longer.

Google Compute offers a sustained use discount for running specific Compute Engine resources a significant portion of the billing month. The discounts come in a couple of tiers and start to apply after running first 25% of a month, then increase after running 50% and 75% of the month. See https://cloud.google.com/compute/docs/sustained-use-discounts

An alternative to the automatically applied sustained use discount is the committed use discount, where signing up for one or three years is awarded with a discount: https://cloud.google.com/compute/docs/instances/signing-up-committed-use-discounts