-자구 is the informal spelling of -자고, proposing something with a bit of bounce: 자 가보자구! 'all right, let's do this.' It sounds lighter and more coaxing than plain -자, which is why hosts use it to sweep viewers along. Add 요 for a polite version — 맛집에 줄을 서러 가시자구요 'let's go queue up at a famous restaurant.'