I did some work myself to supplement Jonah's brilliant, accepted answer. I made a Google Sheets spreadsheet of the data, available here.
I got the weights of all the shotguns and rifles from the manufacturers' websites. I did the same for the four identified handguns, but this left me with at least nine unidentified handguns. Thus, some assumptions were necessary.
I decided to shoot for a valid baseline by supposing that "over a dozen handguns" means "exactly 13 handguns".
To set a minimum weight for the guns, I assumed that there are 9 unidentified handguns, and they are all the same weight as the lightest identified handgun (the Glock 17, at 1.6 lbs/0.73 kg). This gives us a total minimum of 22.6 lbs (10.23 kg) of handguns, and a minimum of 85.1 lbs (38.68 kg) of guns overall.
To set a maximum weight for all the guns, I assumed that there are 9 unidentified handguns, and they are all the same weight as the heaviest identified handgun (the Smith & Wesson Model 586, at 2.6 lbs/1.18 kg). This gives us a total maximum of 31.6 lbs (14.36 kg) of handguns, and a maximum of 94.1 lbs (42.77 kg) of guns overall.
I averaged out the weights of the 4 identified handguns, and came up with a weight of 2.1 lbs (0.95 kg). Multiplying this by the 9 unidentified handguns, I got 18.5 lbs for the unidentified handguns. This gives us a total of at least 26.7 lbs (12.14 kg) of handguns, and a total of at least 89.2 lbs (40.45 kg) of guns overall.
In the interests of a comprehensive answer, I also made a calculation based on the supposition that all of the unidentified handguns would be chambered for the extremely common 9 x 19mm Parabellum round. Averaging the weights of the two identified handguns chambered for 9 x 19mm Parabellum, we get 1.85 lbs (0.84 kg) each; this makes the estimated weight of the 9 unidentified handguns 16.65 lbs (7.57 kg). Thus, we have 24.85 lbs (11.30 kg) of handguns, and at least 87.35 lbs (39.71 kg) of guns overall.
To estimate the likely weight of the guns, I added the weights of the shotguns and rifles to the average of the two estimates for handguns above, and came up with 88.28 lbs (40.13 kg)
Estimated weight of guns: 88.28 lbs (40.13 kg)
Minimum and maximum weight of guns: 85.1 lbs (38.68 kg) to 94.1 lbs (42.77 kg)
This was even trickier, because the only information we have is "700 rounds, assorted." Therefore, I had to make even more assumptions here; this is what I assumed:
The ammunition in the bag is intended for the guns in the bag.
- Five 12 gauge shotguns
- One 20 gauge shotguns
- Eleven 9 x 9mm Parabellum handguns1
- One .357 handgun
- One .38 Special handgun
- One .30-06 rifle
- One .308 Winchester rifle
To set an estimate of the ammo weight, I assumed that Rick took the same number of rounds for each gun. Thus, 700 rounds divided by 21 guns = 33.3̅3̅3 rounds per gun. This means he has 363 rounds of 9mm2, 165 rounds of 12 gauge, and 33 rounds of each of the other calibers3. This gives us an estimate of 35.17 lbs (15.99 kg) of ammo.
To set an upper limit for the ammo weight, I assumed that Rick took 700 rounds of the heaviest ammunition - 2 3/4" 12 gauge shells filled with #00 buckshot. Each shell weighs 1.54 ounces; 700 rounds weighs 67.38 lbs (30.63 kg).
To set a lower limit for the ammo weight, I assumed that Rick took 700 rounds of the lightest ammunition - Hornady 115gr JHP/XTP 9 x 19mm rounds. Each round weighs 0.42 ounces; 700 rounds weighs 18.38 lbs (8.36 kg).
I also decided to average out the upper limit ( 67.38 lbs/30.63 kg) and lower limit (18.38 lbs/8.36 kg), which comes out to 42.88 lbs (19.49 kg).
Likely weight of ammunition: 35.17 lbs (15.99 kg)
Minimum and maximum weight of ammunition: 18.38 lbs (8.36 kg) to 67.38 lbs (30.63 kg)
The Bag itself:
As I said in my question, we're assuming that the empty bag weighs 2 lbs, which is what I found when I looked for heavy-duty duffel bags of similar size and appearance.
Estimated weight of bag: 2 pounds (0.91 kilograms)
Likely overall weight: 125.45 lbs (57.02 kg)
88.28 lbs (40.13 kg) of guns, 35.17 lbs (15.99 kg) of ammo, 2 lbs (0.91 kg) of bag.
Minimum: 105.48 lbs (47.95 kg)
85.1 lbs (38.68 kg), 18.38 lbs (8.36 kg) of ammo, 2 lbs (0.91 kg) of bag
Maximum: 163.48 lbs (74.31 kg)
94.1 lbs (42.77 kg) of guns, 67.38 lbs (30.63 kg), 2 lbs (0.91 kg) of bag
1 Based on the second speculative solution for the weights of the unidentified handguns, mentioned in the "Guns" section - namely, that all the unidentified handguns are chambered for 9 x 19mm Parabellum
2 I found two different weights for two different kinds of 9 x 19mm Parabellum rounds (one weighed 0.42 ounces per round, the other weighed 0.52 ounces per round), and because we don't know which kind Rick took, I averaged them out to 0.47 ounces per round
3 Every caliber and gauge of ammunition comes in different variations, according to powder load, type of projectile, type of casing, etc; I simply used the weights of the most common commercially available variants of everything except the 9mm ammo
4 The TWD wikia identifies more handguns than IMFDb did, but lacks citations, so it is less authoritative. Their list differs from IMFDb in the following ways: four additional Glock 17 9 mm; one Colt Detective Special .38 Special; one Colt Official Police .38 Special; one Browning BDA; and one of the Mossberg 500's is described as a Persuader model.
Based on this, and assuming that there are 2 unidentified 9 mm handguns weighing ~1.83 lbs, and that Rick took 33-rounds per gun, we get a total weight of 122.67 lbs (85.51 lbs of guns, 35.16 lbs of ammo, and 2 lbs of bag). I didn't include these figures in the main text of my answer because I cannot confirm the accuracy of the wiki's information.