I concur with those who are saying that you should do a race before committing money to something you may not end up doing much (but $650 isn’t a huge investment). I’d buy some cheap clip on aero bars and maybe an aero road helmet like the s works evade (which you can wear for anything, even if you don’t do tris or TT’s past the first one).

Regarding weight: aero will 95% of the time incur a slight weight penalty, but weight only really matters on inclines of over 6%. Money wise, it’ll cost you roughly $500 per half lb to drop weight on your bike. It’s easier to lose body weight and ride a lot instead of trying to buy or build a lightweight bike. My race bike is an Allez Sprint, which is aluminum and heavier (but just barely) than most entry level carbon bikes. But it’s aero is the right places and super stiff, so it is able to outperform many carbon bikes at 3x the price (I paid ($1600 for it).

In short: try before you buy. Triathlon and TTs become an arms race that’ll max out your credit card in a heartbeat between gear and race fees. Commit to racing and training, then get the gear. Also, buy used whenever possible. Plenty of good deals to be had by people selling gently used parts.