I'm glad you liked my post and found it informative. These quotes from the article explain staking reasonably, but I can try and clarify further if not.

"Because when you ‘stake’ your HIVE tokens into Hive Power, you’re basically investing it in Hive."

“Staking is basically the same as ‘powering up.’
I have no idea why they use different words for this process. ‘Staking’ means ‘to deposit funds and ‘lock’ them as collateral into the blockchain. Doing this means it’s not readily usable by you, but it is usable by the blockchain. This helps the blockchain. It’s a form of ‘investing’ in the blockchain. It’s like putting your money into a savings account in a bank. The cash isn’t readily usable by you, but the bank can do a lot with it. ‘Staking’ funds into Hive provides a service for the long-term sustainability of Hive. It lets them maintain Hive well for all users. Similar to a ‘interest’ on funds in a savings account, staked funds often ‘gain value’ for the staker as well.”

“Yes, because vested, staked, or powered-up HIVE tokens are just HIVE tokens that I’ve converted into Hive Power, and Hive Power is literally my ‘influence’ on the Hive Social Platform.”

Basically, you are correct, staking more = more influence. Wishing you a great day! 🙏