A smaller flask is of course lighter, but loses heat faster and holds less. Your whole drink strategy needs to be considered.
A litre is a lot though, unless sharing - there's plenty of choice of 500-600ml flasks; one I found easily weighs 300g (compared to 530g for their lightweight 1l model. Thermos, the brand I've linked, has been in the business a long time (since the vacuum part was always silvered glass, visible on the inside) and is synonymous with vacuum flasks in the UK. I wouldn't go smaller than about 500ml as the hold time tends to be too short.
The main loss is at the lid, which is merely insulated. A better quality flask will hold heat better (and may weigh a little less overall). The best lids I've found are those that allow you to unscrew slightly to pour, using all their volume for insulation. I would avoid those with a clever mechanism that traps the dregs of your drink in an inaccessible volume. This means less insulation and also, having opened one up destructively, I never want to drink from anything so filthy again. Regardless of the lid design, supplementing the insulation in this area (wrap it in spare clothing, use an insulated pouch, etc.) will help a bit.
The smaller the flask, the more important it is to preheat it well when you fill it (the surface area to volume ratio is worse, and the steel is the same thickness, so each drop of your drink is heating more steel).
The other important heat loss is opening the flask, letting out hot drink/air/steam and replacing it with cold air. Waiting as long as possible for the first drink helps here. If you're in a group, share out one flask at each stop, keeping the others closed. I'll sometimes save mine until we're nearly done, a habit from winter kayaking when a hot drink borders on being emergency kit if someone gets wet and cold.
Hiking I might be tempted to carry a tiny stove (you could do better than this 60g one I made) for actual emergencies, combined with a smaller flask (and a water bottle, possibly insulated), or, if you drive to your hike, leave a big flask in the car for the end - something else I've done when kayaking.