At lower price points, saving weight usually means spending disproportionately more money. It is easy to get sucked into the cost per gram game, but chasing a few hundred grams of weight loss on an entry-level bike often costs a fortune in upgrades that provide very little real-world benefit.
I have always found that focusing on the basics delivers much better results. Switching from stock rubber to quality performance tyres is the cheapest way to make a bike feel faster, and consistent riding on hills does more for climbing speed than shaving weight off a bottle cage. If you are riding an aluminum frame, you are better off spending your budget on a solid wheel set rather than chasing marginal weight gains.
At what point does the cost of saving weight on a budget bike stop making sense for you?