As he got older his belief in these principles did not_____.

The correct answer is option number - C.

Waver means - To sway back & forth, to fluctuate /vary,to tremble,to flatter,to be indecisive.

Dither- To tremble,the state of being undecided.

Wither-To go against,resist,oppose.

Shake -to cause something to move rapidly in opposite directions,to disturb emotionally,to lose,evade,get rid of

Here sentence implies that -As he got older, beliefs in principles became more strong,he didn't fluctuate.

Remaining options are contextually incorrect.