If you're looking for a meeting place or a good stop around ½ or halfway between Pompano Beach and Weston, you can try Davie, FL, which is about half an hour southwest of Pompano Beach, or about 18 minutes east of Weston.
Another possible place to stop near the midpoint is Fern Crest Village.
About ¼ or a fourth of the way, you can stop at Fort Lauderdale, FL. This is about 10 minutes south of Pompano Beach.
About ⅔ or two thirds of the way, you can stop at Pine Island Ridge, FL. This is about half an hour southwest of Pompano Beach, or about 13 minutes east of Weston.
About ¾ or three fourths of the way, you can stop at Melalevca Isles, FL. This is about half an hour southwest of Pompano Beach, or about 10 minutes east of Weston.
If you drive straight through without stopping at all, the total distance is 30 miles. The distances shown above don't include local roads to get into each town, so if you're planning a long road trip, make sure you factor in traffic and road conditions, rest stop breaks, and interesting detours along the way. If you're in a rush, you can do the trip with zero stops, and your total travel time would be around 39 minutes.