If your goal is to just lose weight, you definitely want to make sure you add jogging/running into your routine. If it's a matter of losing fat or improving your body composition, then that's less important.
If you look at mid- to long- distance runners, their body type is very very lean and wiry. Swimmers, because they are using their upper bodies so much, even if they are very lean, they tend to carry a lot of muscle in the back, chest and shoulders. That muscle = weight. When I used to swim competitively in my high school years, I'd actually gain weight through most of the season from that added muscle (even though I was getting in better shape and losing fat), and then a lot would drop off in the end of the season taper.
As far as weight training goes, you probably want to do more high-rep sets to build some strength, but strength over a prolonged period of time. Being able to push a lot more weight for just a few reps does not translate well in to activities like swimming and non-sprinting running, which are do not require instant, single-explosion effort (except the start, but then you still have the entire race).
Better to work with a lighter weight for 30 seconds (should get 25 reps in that cycle, if you can do it easily, increase the weight. If you're getting to the end and struggling with those last few reps, you've got it about right).
I would run on "off" days when I'm not swimming. Weights, I'd split exercises into torso (chest, shoulders, back) on one day, limbs (arms legs) on the other, and alternate, getting in four or five days a week. Core work - every day.
I prefer weights before swimming, because if I'm fatigued from doing weights, I can still swim, just not as fast a pace on my repetitions, but I still get the overall distance covered. If I'm fatigued from swimming, that means failing to move the weights, and losing that exercise benefit.