Since he's a preterm baby, he's actually just 7 months old developmentally so don't worry too much mommy! He'll eventually catch up (:
Indeed tummy time is really impt as it helps baby to strengthen his neck which is vital for his progression to flipping, rolling and crawling. My baby too hated it at first but I always did it after every diaper change since he was a few weeks old so it's many times per day. Increase duration as he gets stronger. Eventually my baby was alr rolling ard at 3 mo and starting to crawl in reverse at 5+ months.
I do alot of playtime exercises with my baby. You can google it, lots of youtube videos. Can also check out this IG: https://instagram.com/kinactive_kids?utm_medium=copy_link
For the weight part my PD said once baby consumes more solids, the weight will increase. My baby too is just in the 25th percentile for weight, not balanced with his 80th percentile for height but he seems to be gaining more now since he started solids at 5+ mo.