Q: How can i improve my paddling strength when i can only surf at weekends?

I would definitely suggest trying to swim at least 2 x days per week. Try and aim for 45 min durations and then combine with breaking it up into interval training - High intensity interval work. This way, your arms will be ready for the longer paddle sessions as well as the short sharp burst when going for a wave. Try also float work, swimming with a float between your legs and working on paddle strokes only.

You can also build strength and endurance for paddling by weight training. If you are unfamiliar with weight training, then hire a trainer, (even if it is just to get you started) preferably with a surfing or swimming background, to get you conditioned for surfing and give you a programme to condition you fully.

I would also suggest yoga to aid towards the mobility and flexibility of the shoulders. Muscular imbalances and tightness are all going to inhibit your paddling.