ABOARD THE USS GEORGE WASHINGTON—A U.S. aircraft carrier strike force's visit to Manila is the latest show of American military might partly aimed at countering China's grip in Asia. But the nuclear-powered USS George Washington's five-day visit also provides hundreds of Filipino American sailors a chance to soak in the warm embrace of a second home.

The Philippines has reached out to the U.S. for help in modernizing its warships and planes and in training its troops amid renewed entanglement in territorial disputes with China in the South China Sea.

Manila's desire to bolster its defense has dovetailed with America's intention to pivot away from years of heavy military engagement in the Middle East to Asia, where it's trying to foster closer alliances partly as a counterweight to China's rising clout.