I have held a few tikkas and to me personally the feel cheap. I know they are not built cheap because two of my hunting buddies swear by them. I just personally don't like the way they feel.
I know what you mean about the "feel" when you first pick one up. The light weight and very "different" feel of the bolt throw kinda makes if feel less sturdy than say a M-70 or a Weatherby. I easily resisted getting one for a long time, but found myself in need of a replacement for my (until that point) trusty Ruger 30-06 right before caribou season and a deal came up on a Tikka. I grabbed it thinking I could easily re-sell at no loss after the season if I didn't like it. Well... lets just say it grew on me.
I'm pretty opened minded when it comes to trying guns, but pretty picky about function. I've owned one each of Ruger MKI, MKII, Remington 700 , 721, Savage 116, Large and Small ring mausers, Pre and post 64 winchesters, Tikka and even a Sako.
The Tikka feeds better and I can work the bolt from the shoulder faster than my Pre-64, so I've used it on dangerous game without qualm.
The bolt works just as slick at -20 F as it does at +70. More than I can say for the Ruger or the Remington, so it gets used on all my winter hunts.
I've drug it through some really nasty weather and discovered that goofy closed top action works superbly to keep the snow and mud out of the moving parts.
And it's completely non-fussy about loads.
Does this mean that Tikka's are the most awesome rifle around? nahh... Most of the rifles I've owned would have worked. Like I mentioned, I've used a bunch, and was more or less happy with almost all of them. The only one that I really disliked was the Savage, just because it was so crudely built that I had to finish the factories job before it would feed right. Others love them, so maybe I got a lemon.
Like Ross said, it's mostly about having confidence in one one you choose. In my case, the Tikka had to earn that confidence from scratch, since I had the same mis-givings about the way if "felt" when I first picked it up. My use and abuse over the last couple of years have overcome that feeling and now I'm totally confident in it. Buying new you don't have the luxury of a track record with the gun, so if that big Weatherby makes you feel confident, then heck... buy that one. Odds are it will kill things just as dead as a Remington or Winchester or.... Based on my experience with a bunch of brands, it's really hard to go too far wrong with any of the big name rifles for "normal" hunting, so roll with the one that feels right.
The only knock I can think of (besides price) on the Weatherby is the fact that they have blued actions. If you want ALL stainless, then you need to look at another brand. Most are pretty heavy too, but that may not concern you for day hunts.
Yk