BUICK shakes going up very slight grades

1996 Buick Regal w/ big v6. 120k. When traveling on the interstate or other roads with just a slight uphill grade, the front end shakes. From what I can tell, it is the right front side. Not unbalanced tires, because they were balanced and the problem is still there. No CV axle clicking when turning. Could it be a wheel bearing? This happens only after the vehicle has been operated for about 20 minutes in the summer and longer during the cold months. If I push on the acclerator pedal or brake, the shaking stops.