Am I being paranoid

hi everyone I have only been in a relationship for 5 weeks trouble is we tend to see each other only once a week and prob one night over the weekend when he doesn't have his children, also he works nights 2 weeks a month which doesn't help matters. The reason I am being paranoid is if he really liked me and wanted to spend time with me would he not try and make more time to see me or is it normal to spend this much time together when only been going out 5 weeks ??