As @bpsmith mentions, a lighter, better bike will be faster up hills and so will weight loss and improved fitness. You can go for one, t'other or both, but you can't go in to a shop and lose a few kilos of bodyweight in exchange for some cash.
Looking at that bike though, better gearing options would help. This can be achieved by changing the chainset for a compact double or even a tripple. You might even just be able to change the inner chainring for a smaller one.
The cassette doesn't look particularly big either, but you might find you need a new rear derailleur if you change the total max/min tooth count too much. Spacing between gears can also affect your riding in that big jumps between cogs can unsettle your cadence/rhythm, but changing this by adding gears would need a new groupset and possibly wheels.
If you can find a smaller inner chainring it would be a start in the right direction, but if you fancy a new bike anyway, you will take a lot of variables out in one go.
Looking at that bike though, better gearing options would help. This can be achieved by changing the chainset for a compact double or even a tripple. You might even just be able to change the inner chainring for a smaller one.
The cassette doesn't look particularly big either, but you might find you need a new rear derailleur if you change the total max/min tooth count too much. Spacing between gears can also affect your riding in that big jumps between cogs can unsettle your cadence/rhythm, but changing this by adding gears would need a new groupset and possibly wheels.
If you can find a smaller inner chainring it would be a start in the right direction, but if you fancy a new bike anyway, you will take a lot of variables out in one go.