People Staff
April 13, 2013 12:15 PM

From opposite ends of the Ping-Pong table, the famously competitive parents of Britain’s future monarch grinned at each other, and then let fly.

“Ahem, I think that was 6-2,” William said, declaring victory over Kate during their visit to a Glasgow sports center April 4. But, after his official duties were done, he turned to Lord Lieutenant Sadie Docherty, the couple’s host for the day, and chivalrously fessed up: “The only reason I won today was because Catherine was pregnant,” the prince told Docherty, who recounted the conversation to PEOPLE.

“Otherwise she would have taken off her coat and beat me.” That same day, while chatting with homeless youth at a Quarriers shelter, Will praised Kate‘s cooking, pointing to his allegedly expanding waistline.

PHOTOS: Duchess Kate’s Royally Chic Bump

“He isn’t very good in the kitchen,” Kate teased. But as the two wordlessly brushed against each other at every stop on their two-day Scottish tour, the affection and tenderness between them spoke volumes. “The eye [contact], their smiles to each other, were very genuine, very caring,” Paul Moore, Quarriers CEO, told PEOPLE. “You know when you’re in a restaurant and see two people obviously in love? That’s what they’re like.”

A first pregnancy can put any marriage to the test cue the nausea, stressful moments and unforgiving deadline (ready or not…). But well into their second trimester, the royal couple are cruising to parenthood more demonstrably – and demonstratively – in love than ever.

“They’re much more touchy-feely than they were,” observes royal photographer Mark Stewart of Will’s now-automatic protective hand to Kate’s back on official outings. Adds royals author Judy Wade, who has watched the couple for a decade: “They’ve always been close, but it is much more pronounced since she has become pregnant. There appears to be a new, deeper bond between them.”

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