G'day,
I used to lift weights and packed on the kilos... got to a point where it definately affected my surfing. Not just the added bulk, but the 'day after' muscle fatigue from a good weights session...
Cardio training is definately part of it... Paddling technique and your position on the board is a BIGGER part of it.
I'm plenty of kgs over weight and on the wrong side of 40yo but still get my fair share of waves because I can paddle well and know where to position myself in the break relative to the oncoming wave...
One thing that helps is lap swimming. It develops repetitive strength and muscle endurance in the areas you need it. Note that paddling for a wave and swimming (well) are very different - but use the same set of muscles...
Swimming's also a good loosener after all the weights