Should I just keep doing what I'm doing?

Whether 139.4 lbs is healthy or not depends on your height.
If you want a nice body, cardio alone on that bike and more weight loss won't help. Look into lifting and/or strength training with just body weight. Not that cardio is bad at all, but some people think that it's the one thing that'll give them what they want.
Since you make sure to eat back exercise calories sometimes and don't have too large a gap between TDEE and intake, I think your eating ways are okay.
Not losing weight every week is normal. That loss you saw reflects the success of your work during those two weeks when you thought nothing was happening. We sometimes call it a "whoosh."

Overall, I'd say just consider adding strength training of some sort to your routine and try to hit fat and protein goals.
Consistency is key. Also, it's been only two weeks as you said. Keep going for a few more weeks and record your weight to check your rate of loss.

I think 2.6 pounds in two weeks is awesome, especially since you have so little to lose. With your goals, I would 1.) Tighten up my logging with the help of a food scale and being more consistent, 2.) Raise my calories to lose at a rate of .5 pounds a week, and 3.) Start looking into a strength training program to retain muscle while losing fat. Just my two cents. Good luck.

rather than spend money on weights, you might consider starting a bodyweight exercise program. it is a good way to start strength training, doesn't require you to buy more stuff, and can give you a good base for starting a weights-based training program later on. lots of stuff on mfp and the web to get you going.