How far back are the comments you're finding about BW from? It used to be a decent drain on battery a few years back but I've not noticed any drain worth mentioning compared to anything else running on my phone. It's a small enough percentage that it doesn't show up on the stock battery monitor app.
That said, it's possible that battery usage could also be affected by customizations you add to the widget...mine is pretty minimal, all things considered. The bulk of the drain is likely from the weather checking online every so often which will be an 'issue' regardless of the widget you choose.
The best thing to do is probably to try a few free ones for a week or so each and monitor the drain yourself and see what works best for your needs.