Hello,
As someone suggested, everyone out here will have his/her own favorite camera and that's the one they'll recommend. That said, take this and all of these recommendations with that particular grain of salt.
I have two recommendations on camera systems that are not necessarily MY favorite, but which I think will compliment your M3 shooting and give you familiar, if not identical effects.
They are the Leica R3/R4 and the Minolta XG series camerass (particularly the XG-M). Reasons follow.
As was mentioned in another post, the Leica R4 is a great camera. The glass you buy for it will most closely resemble the Summicrons (if that's what you have) that you shoot on your M3. It and its lenses are not inexpensive however. And I think that was a factor you were conscious of in your original post. The R3 is a little older and will cost less than the R4, but still more than most cameras of the same vintage.
My other suggestion is similar to one posted early on. Check out a Minolta camera. If you want light and a bright viewfinder, specifically check out the XG series. They are ridiculously inexpensive and the XG-M will give you full manual metering with a bright matte viewfinder. And they are LIGHT. I don't know the actual grams, but they feel half as light as my Nikon FM.
The other thing you will like about Minolta is that they and Leica worked very closely together in the 70's and early 80's and that is evident in thier SLRs and SLR lenses from that era. If you look at their SLR bodies and lenses you will notice distinct similarities (some would say replications). The XE is from this era and externally is indistinguishable from the R3, as is the R4 from the XD series (there are major differences however once you look under the hood). The Rokkor and Minolta MD lenses are known for having a bokeh (glow) to them that is comprable to that of the Leica RF lenses.
The Minolta lenses cost MUCH less than their German cousins. The Minolta 200mm, f/2.8, while expensive for a Minolta lens costs a fraction of what a Leica SLR lens in the same range will cost. I'm told that the Rokkor 200mm, f/4 mentioned in that earlier post is also a good lens although I have not used it myself.
So, consider the Leica R3 if you want glass that performs as well (and costs as much) as your M mount Leicas. If you want a look as close as you can get without paying for the Leica name, get a lens that was designed in cooperation with Leica and either an XE or XD if you want the Leica feel - or an XG if you don't care what people think and just want the lightest body for that great lens. The good news is that the XG bodies are so cheap used that it might even balance out the difference of getting the 200mm, f/2.8 instead of the f/4. You will get no respect with a Minolta XG, but you will get awesome photos from those Rokkor lenses.
Good luck. Let us know what you ultimately decide.