Were you using the Tamron VC or one of their older models? Without VC/OS/VR or a similar system, I find 70-300mm lenses quite challenging to use handheld on film cameras. None of them are at their best wide open, yet all too often you have to shoot wide open in order to get a high enough shutter speed to overcome camera shake.
I destroyed my 70-300mm ED in a "5 foot drop" test after getting nudged by an inline skater. I tried replacing it with a Tokina 80-400mm, but found that even more difficult to use. I settled on a Nikon 70-300mm VR, which I typically use it as part of a lightweight travel kit. I'm happy with it in that role, but when I expect to be using a longer lens a lot, such as for motorsports, I use a 300mm f/4.
The 100-300mm f/4 suggested by Vanishing Point is quite a bit heavier. Unfortunately, with an N80, using a 14B teleconverter with any lens limits one to unmetered manual exposure only.