Longtime sweethearts Kate Middleton and Prince William have grown closer than ever amid her cancer battle, according to sources who said they have a newfound appreciation for each other as she undergoes treatment. Eyewitnesses couldn’t help but notice the connection shared between William and Kate during her highly anticipated Trooping the Colour appearance on June 15. “Kate was gazing at William,” said a source in Us Weekly’s new report. “They looked all loved up.” It’s been six months since the couple were last seen at an official event and insiders said there was a visible difference in the…